Incoherent/coherent multiplexed holographic recording for photonic interconnections and holographic optical elements

ABSTRACT

The present invention relates to a novel architecture and associated apparatus for the development of highly multiplexed photonic interconnection networks and holographic optical elements with maximum optical throughput efficiency and minimum interchannel crosstalk, based on parallel incoherent/coherent holographic recording and readout principles. This scheme further provides for arbitrarily weighted and independent interconnections, which are of potential importance in the development of neuro-optical computers, as well as photonic interconnection networks and multiplexed holographic optical elements. In addition, the extremely difficult problem of copying the contents of a three-dimensional holographic storage device in one step is soluble by utilization of the architectural principles and specified apparatus that are key features of this invention.

ORIGIN OF INVENTION

The U.S. Government has certain rights in this invention pursuant toContract No. F49620-87-C0007, awarded by the Department of the Air Forceand to Grant No. AFOSR-89-0466, awarded by the Defense Advanced ResearchProjects Agency through the Department of the Air Force.

TECHNICAL FIELD

The present invention relates to multiplexed volume holographicrecording, readout, and interconnections, and, more particularly, tophotonic interconnections, photonic implementations of neural networks,and multiplexed holographic optical elements.

BACKGROUND ART

Research in optical implementations of neural networks has included (1)systems with one-dimensional arrays of neuron units with two-dimensionalinterconnections and (2) systems with both one- and two-dimensionalarrays of neuron units with three-dimensional volume interconnectionmedia. The former approach does not appear suitable, due to inability toscale up to significantly larger networks than those implementable usingelectronics. The latter approach is currently under active investigationin a number of laboratories.

Much of the optical research has been very creative and has addedimportant elements to an understanding of optical neural networkimplementations. Notwithstanding this, however, the current status isthat most three-dimensional optical implementations have been specificto one neural network model, usually an associative memory. To the bestof the inventors' knowledge, none have demonstrated both positive andnegative weights efficiently in a working, scalable system and none havedemonstrated a learning system with a large number of neuron units andindependent interconnections with high connectivity (i.e., with thenumber of independent interconnections much greater than the number ofneuron units).

In any system involving large numbers of operations, such as neuralnetworks, telecommunications interconnections for long distanceswitching, and interconnections in digital computing, it is desirable touse multiplexed volume (thick) holography for storage of theinterconnections, since this permits the storage of much moreinformation than can be done in planar (thin) holograms. In the case ofholographic optical elements, the utilization of a volume holographicmedium permits the encoding of complex space-variant optical functions.

In forming multiplexed volume holograms, one of three approaches istypically taken: (1) sequential, which involves severaltemporally-sequenced (and hence incoherent) exposures of the hologram,done by rotating or translating the hologram (or the source beam or theobject beam); (2) simultaneous and fully coherent, which involves theuse of two or more mutually coherent beams, each encoded withinformation and serving as a reference beam for the other(s); and (3)some combination of sequential and simultaneous fully coherent.

The first approach has the major disadvantage that temporal sequencingis time-consumptive, which can be of considerable importance inapplications envisioned herein, for which the number of independentinterconnections that must be recorded is extremely large. Also, in manyholographic recording materials, sequential exposures tend to erasepreviously recorded information, leading to the necessity ofincorporating unwieldy programmed recording sequences in order to resultin the storage of a predetermined set of interconnections.

The second approach is designed to circumvent the above sequencingdifficulties, but suffers instead from the coherent recording ofunwanted interference patterns (holograms) that give rise to deleteriouscrosstalk among the various (supposedly independent) reconstructions, asdescribed in more detail below.

The third approach is subject both to sequential recording time delaysand the necessity for programmed recording schedules, as well as to thegeneration of undesirable crosstalk. As such, none of the previouslyemployed multiplexed recording techniques allows for the generation ofthree-dimensional, truly independent interconnections between two ormore two-dimensional planar arrays within the context of a temporallyefficient recording scheme.

In all of the prior art approaches to the holographic recording of amultiplexed interconnection, two primary forms of interchannel crosstalkare encountered to a greater or lesser extent. Coherent recordingcrosstalk arises from the simultaneous use of multiple object andreference beams, all mutually coherent with each other. The mutualcoherence causes additional interconnections to be formed other thanthose desired. Reconstruction with independently valued inputs resultsin the generation of output beams that cross-couple through theundesired interconnection pathways which compromises the independence ofthe desired interconnection channels.

A second, unrelated form of crosstalk arises due to beam degeneracy,which occurs whenever a single object beam is used with a set ofreference beams to record the fan-in interconnect to a single outputnode (e.g., neuron unit in the case of the photonic implementation ofneural networks). (Fan-in is the connection of multiple interconnectionlines to a common output node.) This latter form of crosstalk is presenteven when the set of object beams is recorded sequentially.

Of at least equally serious consequence is the optical throughput lossthat results from interconnection fan-in so constructed as to exhibitbeam degeneracy. In many well-documented cases, this loss is severe,resulting in at least an (N-1)/N loss (or, equivalently, a 1/Nthroughput efficiency) for the case of an N-input, N-outputinterconnection system, as reported by J. W. Goodman, Optica Acta, Vol.32, pages 1480-1496 (1985). This is a truly daunting loss factor forinterconnection systems such as those envisioned for neural networks,which may both require and be capable of 10⁵ to 10⁶ inputs and outputs.

In the prior art, few attempts have been made to address the extremelyimportant technological problem of duplicating the contents of a fullyrecorded, heavily multiplexed volume holographic optical element orinterconnection device, particularly in the case of neural networkinterconnections. For example, to the inventors' knowledge, there is noknown prior technique for rapid copying of a volume hologram that isangularly multiplexed in two dimensions.

In the case of neural network interconnections, the training and/orlearning sequences may be quite involved; in some cases, the trainingand/or learning sequences may result in a unique interconnection, whichmay not be reproducible in and of itself at all. In such cases, it isdesirable to replicate the contents of the interconnection medium insuch a manner that a fully functional copy is produced, as characterizedby a complete operational set of interconnections indistinguishable fromthose implemented from the master. The method of replication must notdemand an extremely lengthy recording sequence, must not be inefficientin its utilization of the programmed recording schedule and/or the totaloptical energy available for reproduction purposes, and must not induceadditional optical throughput loss or interchannel crosstalk beyond thatalready incorporated in the master.

It is to these ends of producing a method for holographically recordingcomplex interconnection networks and holographic optical elements in atimely manner without significant interchannel crosstalk and/or fan-inloss that the invention described herein is directed.

DISCLOSURE OF INVENTION

In accordance with the invention, incoherent/coherent multiplexedholographic recording for photonic interconnections and holographicoptical elements is provided. As a part of the invention, apparatus forproviding multiplexed volume holographic recording comprises:

(a) means for providing an array of coherent light sources that aremutually incoherent;

(b) means for simultaneously forming an object beam and a reference beamfrom each coherent light source, thereby forming a set of multiplexedobject beams and a separate set of multiplexed reference beams;

(c) means for either independently modulating each object beam, orspatially modulating a set of object beams so that all object beams areidentically modulated;

(d) means for either independently modulating each reference beam, orspatially modulating a set of reference beams so that all referencebeams are identically modulated;

(e) a holographic medium capable of simultaneously recording therein aholographic interference pattern produced by at least a portion of theset of all modulated multiplexed object beams and of the set of allmodulated multiplexed reference beams pairwise, with all such pairsbeing mutually incoherent with respect to one another; and

(f) means for directing at least a portion of the set of modulatedobject beams and of the set of modulated reference beams onto theholographic medium and for interfering the portion of the modulatedbeams and of the set of modulated reference beams, pairwise, inside theholographic medium.

Although the primary mode of multiplexing is angular, spatial and/orwavelength multiplexing may also be incorporated.

Further in accordance with the invention, the above apparatus isprovided with means for blocking the set of object beams such that atleast a portion of the set of reference beams (either modulated orunmodulated) reconstruct a stored holographic interference pattern. Inone embodiment, the reconstructed pattern is angularly multiplexed anddetected in such a manner as to produce an incoherent summation on apixel-by-pixel basis of the reconstructed set of object beams. In thismanner, multiplexed volume holographic recording and readout areprovided.

Specific implementations to neural networks, telecommunicationinterconnections (e.g., local area networks and long distanceswitching), interconnections for digital computing, and multiplexedholographic optical elements are provided.

In addition, apparatus for copying a multiplexed volume hologram isprovided, comprising:

(a) means for providing an array of coherent light sources that aremutually incoherent;

(b) means for forming two reference beams from each coherent lightsource, thereby forming two sets of multiplexed reference beams, eachset at a different location;

(c) means for directing the first set of reference beams onto theoriginal multiplexed volume hologram to thereby form a set of outputbeams;

(d) means for directing the second set of reference beams onto asecondary holographic recording medium;

(e) means for directing the set of output beams from the originalmultiplexed volume hologram onto the secondary holographic recordingmedium, with path lengths sufficiently identical to the reference beampath lengths to permit coherent interference, pairwise, between theoutput beams and the second set of reference beams, inside the secondaryholographic recording medium; and

(f) means for simultaneously recording in the secondary holographicmedium a holographic interference pattern produced by the set of outputbeams and the second set of reference beams, thereby forming thesubstantially identical multiplexed volume hologram.

Also, novel spatial light modulators used in the practice of theinvention are provided, combining means for modulating a first set oflight beams, means for detecting a second set of light beams, andelectronics for altering the modulation in response to the detectedbeams. The novelty is achieved by modifying either the functionality orthe configuration of the spatial light modulators described in the priorart.

The architecture and apparatus of the invention significantly reducecoherent recording crosstalk and beam degeneracy crosstalk, and permitsimultaneous network initiation, simultaneous weight updates, andincoherent summing at each output node without significant fan-in loss.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a generalized interconnection, with both fan-out and fan-in;

FIG. 2 is a schematic diagram of fan-out, showing interconnectionpathways and the implementation of analog weights;

FIG. 3 is a schematic diagram of fan-in, showing interconnectionpathways and the implementation of analog weights;

FIG. 4 is a schematic diagram of optical apparatus for simultaneousincoherent/coherent recording of multiplexed holograms, showing angularmultiplexing of the reference beam set;

FIG. 5 is a schematic diagram of optical apparatus for eithersimultaneous or independent readout of multiplexed holograms showingmutual incoherence of readout (reconstructed) beams;

FIG. 6A is a schematic diagram of optical apparatus for recording ofdoubly angularly multiplexed holograms, each a hologram of a 2-D arrayof pixel values, while FIG. 6B is a schematic diagram of that portion ofthe apparatus of FIG. 6A, used in the reconstruction of the recordedimages, showing the incoherent summation on the output plane of the setof reconstructed images in pixel-by-pixel registry;

FIG. 7 is a schematic diagram of optical apparatus for one-step copyingof the entire multiplexed holographic record, showing the use ofsimultaneous readout by means of mutually incoherent readout beams;

FIG. 8 is a schematic diagram of the optical interconnection paths dueto a holographic interconnection architecture for the 3:3 fan-out/fan-incase, constructed such that each input and output node is only singlyangularly encoded, showing the origin of crosstalk and throughput lossdue to beam degeneracy;

FIG. 9, on coordinates of diffraction efficiency and normalized gratingstrength (v/), is a simulation result for the holographicinterconnection architecture of FIG. 8 utilizing the optical beampropagation method, for the case of sequential recording of theinterconnection gratings, showing the ran-out loss;

FIG. 10, on coordinates of diffraction efficiency and normalized gratingstrength (v/), is a simulation result for the holographicinterconnection architecture of FIG. 8 utilizing the optical beampropagation method, for the case of simultaneous fully coherentrecording of the interconnection gratings, showing the fan-outthroughput loss and the occurrence of recording-induced crosstalk;

FIG. 11 is a schematic diagram of optical interconnection paths of theapparatus described in FIG. 6 for the 3:3 fan-out/fan-in case, showingthe angular multiplexing of both object (source) and reference beamsets, configured to produce angular multiplexing of the reconstructionbeam fan-in to a given output node;

FIG. 12 is a schematic diagram of a multi-function spatial lightmodulator, as utilized in the interconnection architecture shown in FIG.14, showing the incorporation of multiple photosensitive elements,control electronics, and multiple modulation elements within each pixel;

FIG. 12A is an enlargement of a portion of FIG. 12;

FIG. 13, on coordinates of voltage (ordinate) and voltage (abscissa), isa plot of output transfer characteristic curves for both outputs of adual rail CMOS differential amplifier, with 15 transistors in an area of2500 μm² ;

FIG. 14 is a schematic diagram of a preferred embodiment of apparatusfor the implementation of neural network modules, for the case ofHebbian learning;

FIG. 15 is a schematic diagram of a preferred embodiment of apparatusfor the implementation of neural network modules, for learningalgorithms of the form Δw_(ij) =αx_(i) δ_(j) ;

FIGS. 16A-C are schematic diagrams of preferred embodiments of means forgenerating learning terms δ₁, for the cases of (A) Widrow-Hoff, (B)Perceptron, and (C) back propagation learning;

FIG. 17 is a schematic diagram of an alternative embodiment of apparatusfor the implementation of neural network modules.

FIG. 18 is a schematic diagram of apparatus for switching from a set ofwavelength division multiplexed optical input lines to a set ofwavelength division multiplexed optical output lines, wherein the sourcearray and two spatial light modulators are used to control the routingof the switch;

FIG. 19A is a schematic diagram of means for providing the source arrayof FIG. 18 in the case of a 1-D wavelength division multiplexed (WDM)input line array and a 1-D wavelength division multiplexed output linearray, showing the center optical frequency ν increasing along onedirection and the incorporation of mutual incoherence within a frequencyband Δν about each central optical frequency ν along a different,substantially orthogonal direction, while FIG. 19B is a schematicdiagram of an alternative embodiment utilizing a one-dimensional sourcearray, with center frequency of each element being different, and aone-dimensional phase modulator array providing mutual incoherence;

FIG. 20 is a schematic diagram of means for providing the source arrayof FIG. 18 in the case of a 2-D WDM input line array and a 2-D WDMoutput line array, showing a 2-D laser diode array each element of whichhas a different center frequency, and a modulator array;

FIG. 21 is a schematic diagram of method and apparatus for recording ofmultiplexed volume holographic optical elements, with one set of beamsmodulated independently and the other set of beams modulated spatiallybut identically; and

FIG. 22 is a schematic diagram of method and apparatus for recording ofmultiplexed volume holographic optical elements, with both sets of beams(reference and object) modulated independently.

BEST MODES FOR CARRYING OUT THE INVENTION A. GENERAL 1. Introduction

The description which follows is primarily directed to neural networks.However, it will be appreciated by those skilled in the art that a majorcomponent of the architecture and apparatus is generic to a number oftechnologies, including telecommunications, digital computing, andholographic optical elements. Specific applications to these arediscussed below.

In considering the teachings of the invention, it is essential todifferentiate between two basic types of optical interactions (asdetermined by the nature of the optical signals involved): incoherentand coherent. Incoherent interactions occur whenever the input signalstemporally dephase over the relevant time of observation (detectortemporal integration window), in that they are either broadband (notmonochromatic) or are narrow band (nearly monochromatic) but separatedin optical frequency by more than the inverse of the observation time.

Interactions in which the input optical signals spatially dephase overthe spatial aperture of the relevant detector wherever the output isutilized (detector spatial integration window) are also incoherent forall practical purposes, and will obey certain summation rules. Coherentinteractions occur, on the other hand, whenever the input signalssimultaneously maintain a constant phase relationship over the detectorspatial and temporal integration windows.

From these remarks, it can be seen that it is quite important tounderstand the distinction between coherent (or incoherent) light andcoherent (or incoherent) interactions as defined by the eventualdetector configuration and operational parameters. For example, it isperfectly acceptable to consider a situation in which two mutuallycoherent (temporally) optical beams interact to produce an interferencepattern with a spatial scale small compared with the relevant detectoraperture. In such cases, the interaction will in fact follow incoherentsummation rules, as the detector effectively integrates the spatiallyvarying interference pattern to produce exactly the same result as theinteraction of two mutually incoherent (temporally) optical beams.

Referring now to the drawings, wherein like numerals of referencedesignate like elements throughout, FIG. 1 depicts a generalizedinterconnection scheme, showing both fan-in of input beams 10, 10, tonodes 12, 12', respectively, and fan-out of output beams 10', 10" fromthe nodes.

The section of the interconnection shown depicts the fan-in to them^(th) node from the (m-1)^(th) node plane (not shown), a fullyconnected layer in which the interconnections fan out from each node 12labeled 1 through N to the nodes labeled correspondingly 1 through N inthe (m+1)^(th) node plane wherein full fan-in is effected, and fan-outfrom the (m+1)^(th) node plane to the (m+2)^(th) node plane (not shown).In some interconnection schemes, the m^(th) node plane and the(m+1)^(th) node plane are one and the same, consisting therefore of aset of nodal outputs fully interconnected to the corresponding set ofnodal inputs in a feedback arrangement.

The weights w_(ij) are shown to indicate that each (analog)interconnection path modifies the output from a given node by means ofthe multiplication weight before fan-in is performed with an appropriatesumming operation at each node input. The weight labeling schemeemployed is as shown, such that the weight w_(ij) interconnects thej^(th) nodal output in a given plane to the i^(th) nodal input in thesucceeding plane.

FIG. 2 depicts fan-out of a plurality of output beams 10' from a node 12(i.e., the i^(th) node) on which at least one input beam 10 is incident.Each beam 10' is propagated to the next node with a separate andindependent analog weight w_(ij) as noted above, which is assigned toeach interconnection path.

As depicted in FIG. 2, for the purposes of this invention, the outputvalue from each given node is common, such that the interconnectionsrepresent true fan-out rather than the individual interconnection ofmultiple output ports from a single node.

FIG. 3 depicts fan-in of a plurality of input beams 10 to node 12,generating at least one output beam 10'. Each beam 10 is modified by aseparate and independent analog weight w_(ij), assigned to eachindependent interconnection path. True fan-in is achieved by means of anappropriate summation rule at a single node input, as shown in theFIGURE.

In FIGS. 1, 2, and 3, the triangular symbol utilized to depict eachinterconnection node represents not only the indicated direction of dataflow through the node, but also the potential for incorporation of aninput-to-output control transfer function (e.g., a hard or softthreshold in the case of a neural network) that operates on thefanned-in, summed inputs to produce a single (usually analog) outputvalue that is fanned out in turn to the succeeding network stage.

FIGS. 4 and 5 depict schematically how recording (FIG. 4) andreconstruction (FIG. 5) of a set of holograms is accomplished inaccordance with the invention. In FIG. 4, an array of coherent butmutually incoherent sources 14 generates a set of beams 10 (two suchbeams 10a, 10b are shown). A beam splitter 16 forms a set of objectbeams 11 and a set of reference beams 13. The object beams 11 passthrough a set of objects (A₁, A₂) 18 to form a set of object-encodedbeams 15, which impinge on a holographic recording medium 20. Thereference beams 13 are reflected from a set of mirrors 22 and alsoimpinge on the holographic recording medium 20, where they interferewith the object-encoded beams 15 pairwise to form holographicinterference patterns in the recording medium, as is well-known.

It will be noted that the foregoing apparatus permits simultaneousrecording of the objects. Further, a first light source 14a in thesource array 14 is used to generate a first set of two beams 11a and 13awhich are mutually coherent; these beams derive from beam 10a. A secondlight source 14b in the source array is used to generate a second set oftwo beams 11b and 13b, which are also mutually coherent; these beamsderive from beam 10b. However, since the two light sources 14a and 14bare mutually incoherent, then beams 10a and 10b are mutually incoherent,and the two sets of beams derived therefrom are also mutually incoherentand hence do not mutually interfere to form an interference pattern inthe holographic storage medium 20. While only two light sources 14a, 14bare described, there are, of course, a plurality of such light sourcesin the source array 14, each generating a coherent pair of object andreference beams, each pair incoherent with all other pairs.

Finally, each of the set of object beams and each of the set ofreference beams is independently multiplexed in at least one of angle,space, and wavelength.

In FIG. 5, readout, or reconstruction, is achieved by blocking theobject beams 11. In the case of a holographic optical element, theholographic medium 20 may be read out in a physically distinct opticalsystem, in which the reference beam phase fronts illuminating theholographic medium approximate those of the recording system. Readoutmay be simultaneous and independent, or individual.

In simultaneous and independent readout, output beams 10a' and 10b' aremutually incoherent, and complete control of what is read out isprovided; that is, one-half of beam 13a and all of beam 13b, or all ofbeams 13a, 13b, and 13c (not shown), or other combinations may becontrollably used as readout beams, with the modified set ofreconstructed output beams incoherently superimposed in space. Forclarity, beam 13c is omitted from the drawing. If shown, it would be atyet a different angle from beams 13a and 13b.

In individual readout, any individual readout beam 13j can be modulatedand utilized to reconstruct an individual output beam 10a' or 10b' (or10c', etc.) without significant crosstalk.

Virtual images A₁ ' and A₂ ' are generated from the reconstructionprocess in the position designated 18' where the objects 18 were locatedduring the recording process, in such a manner that the reconstructions10' appear to emanate from the virtual images. A key point is that theset of reconstructed images 10' are all mutually incoherent, and henceobey incoherent summation rules in any chosen output plane, as describedin more detail below.

FIG. 6A depicts apparatus suitable for the simultaneous recording ofdoubly angularly multiplexed holograms, with each hologram comprising a2-D array of pixel values. A shutter 24 in the path of the set of objectbeams 11 is used to control passage of the set of object beams to theholographic recording medium 20. During recording, the shutter 24 isopen. The set of object beams 11 passes through a lens 26, whichapproximately collimates the set of beams and directs them toward afirst spatial light modulator (SLM) 28. Thus, each pixel of modulator 28has many mutually incoherent optical beams (angularly multiplexed)passing through it. The set of modulated beams {A_(j) }is incident onthe holographic recording medium 20.

The set of reference beams 13 passes through lens 30 and lens 34,reflecting from mirror 22 in the process; their function, together, isto focus each beam onto the corresponding pixel of modulator 32. Fromthe spatial light modulator 32, the set of reference beams 13 isdirected into the holographic recorded medium 20 by lens 36, where thereference beams interfere with the object beams to produce a multiplexedhologram with a set of stored interconnection weights. Theinterconnection weights can be dependent on corresponding products ofthe form A_(j) x_(j), as described above.

Finally, it will be noted that the object beams 11 are all at differentangles with respect to each other and that the reference beams 13 arealso all at different angles with respect to each other. As aconsequence of this angular difference, it will be appreciated thatthese beams are double (meaning both object and reference beams)angularly multiplexed in the volume hologram 20.

FIG. 6B depicts the apparatus of FIG. 6A, but with the shutter 24closed, to permit reconstruction of the recorded holograms to generate aset of output beams 10', representing a set of virtual images 18', whichis passed through a lens 38 and imaged onto an output plane 40. Eachpixel of the superposition image in output plane 40 receives anintensity given by the incoherent summation of a number of terms, thenumber given by the fan-in to that pixel, which is equal to the numberof elements in the source array for the case of fully connectednetworks. Each individual term in the incoherent summation is in turnthe product of a stored interconnection weight w_(ij) multiplied by theintensity of the corresponding reference beam x during readout. Hence,the superimposed reconstructions of the separate stored holograms(generating the set of virtual images 18') are incoherently summedpointwise (on a pixel-by-pixel basis in registry).

This incoherent/coherent technique reduces the number of spuriousgratings written, thereby reducing crosstalk compared with fullycoherent simultaneous recording techniques.

2. Source Array

As discussed a critical and novel component that leads directly to theunique capability for simultaneous recording of the holograms is a 2-Dsource array 14, the light emission/reflection from which must becoherent within each pixel but mutually incoherent among all pixels. Thearray size will be determined by the array sizes of the SLMs employed inthe architecture, as these will in fact delimit the space-bandwidthproduct of all of the arrays. Given the geometrical and powerdissipation constraints inherent in the preferred SLM design employedherein, array sizes of ≈10⁴ to 10⁵ elements per cm² are currentlyappropriate. Given further the unique interconnection recordingconfiguration proposed herein, larger array sizes can be configured bymosaic techniques, as the interconnection architecture automaticallycompensates for irregularities in source location.

There are at least three possible structures that can satisfy thenecessary source array requirements. The first is an array of opticallyisolated surface-emitting semiconductor lasers, with adequate pixelationto eliminate the potential for inadvertent phase locking.

Let Δν be the processing-variation-induced or designed difference incenter frequencies from one source to the next. The mutual coherencetime between sources is determined by the optical bandwidth of thesources (in the case of such bandwidth being greater than Δν) or by Δν(in the case of Δν being greater than the individual source bandwidth).

For typical semiconductor lasers fabricated in the GaAs/AlGaAs system,for example, linewidths of 3 nm are common, which corresponds to afrequency bandwidth of approximately 1 THz. Over time scalescharacteristic of currently-available photorefractive volume holographicoptical interconnections, about 1 msec for power levels characteristicof semiconductor laser sources, this large bandwidth will assure mutualincoherence of the array elements. Total power dissipation assuming 1 mAthreshold laser diodes will be under 10 W/cm², and even then willrequire careful heat sinking and attention to thermal design. Theessential advantages of this approach are the anticipated very highresultant optical intensities of ≈5 W/cm² that will in turn acceleratethe holographic interconnection recording (and copying) process, and thesignificant technical leverage enjoyed by this approach due tosubstantial interest in semiconductor laser arrays for a wide range ofpotential applications.

For example, vertically emitting semiconductor laser arrays withdensities of over two million individual lasers per square centimeterhave been fabricated and evaluated successfully, as reported by J. L.Jewell et al, Optics News. pages 10-11 (December 1989). These arrays,however, have not been specifically designed to assure mutualincoherence among all of the individual source array elements, which isa critical feature utilized in the practice of this invention.

The second source array structure employs a pixelated piezoelectricmirror with an intentionally incorporated space-variant non-uniformity.The array is driven such that each individual high-Q mirror element isbrought into resonance at its natural (and distinct) center frequency.For such an array with 10' elements, each separated by ≈2 kHz to satisfythe mutual incoherency requirements of the holographic interconnect, therequired bandwidth is only 20 MHz. This approach has the advantage ofpotentially very high reliability, with capability for reflectingessentially arbitrarily intense CW or pulsed source beams over a broadwavelength range.

The third source array structure is directly derived from the III-Vcompound semiconductor-based or other equivalent spatial lightmodulators discussed below. In this case, a pure phase modulatorgenerates the requisite frequency modulation to guaranteeelement-to-element mutual incoherence. Frequency separations aregenerated by replacing the detector/electronics combination associatedwith each pixel by an electronic ring oscillator or astablemultivibrator with process-variable-induced spatial inhomogeneities inthe center frequencies across the array. The most demanding requirementfor this application is the necessity of achieving greater than phasevariation with minimal associated amplitude modulation. This in turnwill require Δ(nd) products greater than 1/2 (optical path lengthdifferences given by either a change in the refractive index nmultiplied by the active device thickness d, or a change in devicethickness or displacement multiplied by the effective refractive indexof the active region, or both). Such Δ(nd) products may prove to bedifficult to achieve, for example, in traditional multiple quantum well(MQW) spatial light modulators based on the compound semiconductorsystem, and may require the utilization of unusually large piezoelectriceffects in strained layer superlattices, or the incorporation of coupleddouble quantum wells (CDQWs) in modulation doped NIPI structures orplanar asymmetric Fabry-Perot cavities.

Implementation utilizing a wide variety of candidate spatial lightmodulator technologies such as liquid crystal light valves or deformablemembrane devices may prove particularly suitable for generation of thedegree of mutual incoherence required of the source array.

3. Copying of Multiplexed Volume Holograms

Also in accordance with the invention, apparatus for copying an originalmultiplexed volume hologram to form an identical multiplexed volumehologram is provided. The apparatus and method for copying a multiplexedvolume hologram of planar objects that are reconstructed as virtualimages is described first, followed by a description of itsgeneralization to multiplexed volume holograms of planar amplitudeobjects, phase objects, 3-D objects, and multiplexed volume hologramsthat reconstruct real images.

The apparatus is schematically depicted in FIG. 7 and employs theoriginal multiplexed volume hologram 20 (master) to generate asubstantially identical secondary multiplexed volume hologram 120(copy). An array 14 of coherent light sources that are mutuallyincoherent is employed, as described above. A beam splitter 116 is usedto form two reference beams 113a, 113b, from each coherent light source14a, 14b, etc., thereby forming two sets of angularly multiplexedreference beams, each set at a different location, but otherwisesubstantially identical. The first set of reference beams 113a isdirected onto the original multiplexed volume hologram 20, such as bylens 42, to thereby form a set of output beams 110'. The second set ofreference beams 113b is directed onto a secondary holographic recordingmedium 120. In certain applications pertinent to the invention, the twosets of reference beams may be either wavelength multiplexed orspatially multiplexed or any combination of angularly, spatially, andwavelength multiplexed.

Reference beams 113b are made to have phase fronts at recording medium120 that are substantially identical to the phase fronts of referencebeams 113a at the recording medium 20. This can be provided, forexample, by relay optics 44, 46, and 48. If lenses 44 and 46 each havefocal length f then the optical distance from source array 14 to lens ₄,from 44 to 46 is 2f₄, and from 46 to I₃ is f₄, where I₃ is an image ofthe source array. The optical distance from source array 14 to hologram20 is equal to the optical distance from I₃ to recording medium 120. Theposition of lens 42 with respect to hologram 20 is the same as theposition of lens 48 with respect to recording medium 120. Beamsplitter116 and reflecting surface 50 direct the reference beams 113 in thedesired directions. Thus, the optical path from beamsplitter 116 tohologram 20 is essentially identical to that from mirror 50 to recordingmedium 120.

The set of reconstructed output beams 110' is directed from the originalmultiplexed volume hologram 20 onto the secondary holographic recordingmedium 120, such as by lenses 52, 54, with path lengths sufficientlyidentical to the reference beam path lengths to permit coherentinterference, pairwise, between the output beams and the second set ofreference beams, inside the secondary holographic recording medium.

In FIG. 7, plane I₁ corresponds to the virtual image plane of theobjects, obtained from the reconstructed beams of the holograms recordedin the medium 20. (Extensions to non-planar objects are given below.)The images in I₁ can be completely overlapping (as in the case of FIGS.6A and 6B), partially overlapping, or non-overlapping in space (as inthe case of FIGS. 4 and 5).

Lenses 52 and 54, of focal length f, are chosen to create an image ofplane I₁ at plane I₂. In this embodiment, plane I₁ is chosen to becoincident with the virtual image plane of the hologram. Plane I₁ existsat a distance Z₀ from the entrance face of the hologram 20, and theimage plane I₂ of I₁ exists at the same distance Z₀ from the entranceface of the holographic recording medium 120.

Due to the geometry of relay optics 52 and 54, the beams from I₂ areincident on recording medium 120 with substantially identical phasefronts as the original (primary) object beams were incident on hologram20, with the exception of an exact spatial inversion about the opticalaxis. (Such spatial inversion can be removed, if desired, by insertinganother f-2f-f optical relay system in path 110', from I₂ to anotherreal image plane I₂ ', The path of the reference beams 113b is similarlychanged if needed to maintain the requisite pairwise coherence. In theremainder of this section on copying, the light distribution at I₂ thatis subsequently incident on the holographic recording medium will bereferred to as if it were not spatially inverted, with the understandingthat if a non-inverted copy is desired, the optics can be changed asdescribed above.

A set of holographic interference patterns is then simultaneouslyrecorded in the secondary holographic medium 120 by the set of outputbeams 110' and the second set of reference beams 113b, thereby formingthe substantially identical multiplexed volume hologram.

Applications and extensions of this copying apparatus and method toother types of multiplexed holograms will now be discussed. First, allof the copying methods and apparatus described herein apply tomultiplexed holograms originally recorded simultaneously with an arrayof individually coherent but mutually incoherent sources; in this case,the copying apparatus reference beams 113a must approximate thereference beams 13a used during the original recording of hologram 20.In addition, these methods and apparatus also apply to sequentiallyrecorded multiplexed volume holograms, since the net result within themedium is an incoherent superposition of the holographic interferencepatterns. Again, the copying can be made in one step, the requirementbeing that the set of reference beam phase fronts at hologram 20 duringcopying approximate the set of reference beam phase fronts that wereused over time during recording of the original hologram.

The same holographic recording apparatus and method described above cancopy multiplexed volume holograms of a set of planar phase objects thatwere recorded, for example, using a phase modulator at location 28 ofFIG. 6A. This is possible because the imaging optics 52 and 54 in effectcopy not only intensity information but also phase information from I₁to I₂. This further permits generalizations to multiplexed volumeholograms of 3-D objects (again, of a set of original stored hologramsthat was simultaneously or sequentially recorded), wherein the phasefronts from I₁ have been relayed to I₂ (or I₂ ', in the case of havingno inversion). In this case, the plane I₁ represents the intensity andphase information of each beam propagating from each of the original 3-Dobjects.

This apparatus and method can be extended to copies of holograms thatreconstruct real images. Conceptually, in this case, the plane I₁ islocated a distance Z₀ after hologram 20, and the subsequent relay optics52, 54 are positioned the same, relative to I₁, as in FIG. 7. Similarly,I₂ (or I₂ ') is positioned the same, with respect to recording medium120, as I₁ is positioned with respect to hologram 20.

It should be noted that Z₀ does not have to be chosen exactly asdescribed above; in fact, depending on aberrations and apodizationeffects, Z₀ can, in many cases, be set equal to 0 (so that in the caseof planar objects, for example, I₁ is not coincident with the virtualimage plane of the recorded objects).

By incorporating independent control of the sources in the source array,subsets of the original multiplexed hologram 20 can be copied ontorecording medium 120. This is useful, for example, in a manufacturingenvironment in which different copies are meant to have differentholographic recordings, each a subset of the set of holographicrecordings encoded in master, complete multiplexed hologram. The sourcesin array 14 that correspond to the desired holograms to be copied areturned on, and the others are left off. Alternatively, a spatial lightmodulator can be employed in conjunction with a lens to modulate animage plane of the source array 14, in order to provide independentsource control.

This functionality is also useful in the cases of interconnectionnetworks and neural networks, in which a portion of the master hologramis to be copied, to be later used to refresh that part of the originalhologram. Alternatively, the copy can be used as the interconnectionhologram, and the master as a library of interconnection patterns,subsets of which are loaded into the copy 120 to implement a desiredinterconnection.

Finally, it will be appreciated that the apparatus and method can alsobe used to make non-identical copies, in which there is magnification ofthe spatial extent of the stored images by incorporating opticalmagnification into the path 110' (or magnification of angles byincorporating optical demagnification into path 110'). Alternatively,the reference beam illumination of the copy 120 can be changed relativeto the original by changing the phase fronts incident on the copy. Thisis needed for applications in which a set of hard-to-generate storedpatterns are to be transferred from a master multiplexed hologram to acopy, but the copy is to be used in an optical system that utilizes adifferent set of reference beams to recall the stored holographicimages. In this case, the optics in path 113b are chosen to make thephase fronts incident on recording medium 120, substantially identicalto the desired new reference beam phase fronts that will be used toreconstruct the copy. In these non-identical copying cases, the newoptics must be chosen so that the optical path length constraint betweenreference beams and object beams, pairwise, is still satisfied, toassure interference between the mutually coherent beams pairs.

A furtherance of the capability to make non-identical copies is that ofwavelength conversion, in which the recording wavelength generated bythe source array is not the same as the wavelength to be utilized inreconstruction. This feature is particularly useful in the case ofcurrently-available photorefractive volume holographic recordingmaterials, which can be non-destructively read out (reconstructed) onlyat a wavelength of relative photorefractive insensitivity. In this case,the Bragg condition can be satisfied by altering the scale of the sourcearray used for copying in comparison with the scale of the source arrayused for subsequent reconstruction, and by reconfiguring the opticsbetween the source array and the holographic recording medium.

4. Comparison of Architecture of the Invention with PreviousApproaches--Simulation Results

FIG. 8 schematically illustrates what would happen in the case of usingthe sets of object and reference beams 11, 13, respectively, in an N:Nfan-out/fan-in case, of which a 3:3 fan-out/fan-in case is shownexplicitly. The beams 13 comprise the three reference beams x₁, x₂, andx₂ (shown explicitly), among others indicated by the set of three dots).Object beams 11 comprise y₁, y₂, and y₃ (shown explicitly), amongothers. It is desired to record a fully connected interconnectionpattern, with an independent interconnection weight established betweeneach "input" x_(j) and each "output" y₁. In FIG. 8, dashed linesindicate the presence of beams employed at some point during therecording cycle, while solid lines indicate a specific readout examplein which only the beam x₁ is used as an input, generating the zerothorder beams x₁ ', x₂ ', and x₃ ', as well as the output (reconstructed)beams y₁ ', y₂ ', and y₃ '. As will be shown in FIGS. 9 and 10, sucharrangement, typical of the interconnection schemes investigated in theprior art, is subject to a throughput loss (optical inefficiency) ofsignificant magnitude when each common object beam such as y₁, y₂, or y₃is utilized to record either simultaneous (coherent or incoherent) orsequential (incoherent) interconnections with either a full or partialset of reference beams x₁, x₂, and x₃, and the readout is performed withmutually incoherent reference beams. In this case, readout with two ormore reference beams creates equally many beams propagating in eachoutput direction y₁ '. Such output beam directions for any given outputbeam y₁ ' are hence degenerate, and the throughput loss is in factdirectly attributable to this beam degeneracy. Throughput losses willalso be observed with the readout is performed with mutually coherentreference beams if the recording process was performed eithersimultaneously with mutually incoherent reference beams, or sequentiallywith independent reference beams. Furthermore, these interconnectionschemes are subject to both a significant throughput loss and coherentrecording crosstalk when the same sets of interconnections are recordedsimultaneously with mutually coherent sets of reference and object beams(such as y₁ with x₁, x₂, and x₃).

In the discussion of phase volume holographic recording, a quantity ofimportance is the strength v of a given recorded holographic grating,which is defined as

    v=(2π/λ) Δn d

in which λ is the wavelength utilized for holographic gratingreconstruction, d is the effective thickness of the holographicrecording medium, and Δn is the amplitude of the modulated index ofrefraction associated with this given grating, such that the spatialdependence of the local index of refraction on the spatial coordinate xis given by:

    n(x)=Δn sin (2πx/λ).

In the case of either incoherent or coherent recording with incoherentreadout of the interconnection gratings, fan-in throughput loss isobserved. In this example, the weights are in the ratio of 1:2:3 (w₁₁:w₂₁ :w₃₁). In addition, the remaining interconnection weights have beenrecorded such that w_(1j) :w_(2j) :w_(3j) are also in the ratio 1:2:3for j=2,3 and w₁₁ =w₂₂ =w₃₃.

The results of simulations utilizing the optical beam propagation methodare given in FIG. 9, which shows that the ratio of the fan-out (here,1:2:3) is retained; however, the total efficiency (0.06+0.09+0.18) isconsiderably less than 1, due to the throughput loss from thetransmitted zeroth order beams 210' (a direct result of beamdegeneracy). This can be simply explained by reference to FIG. 8, fromwhich it can be inferred that reconstruction beams 10' comprisingoutputs y₁ ', y₂ ', and y₃ ' are automatically Bragg matched to theinterconnections recorded between x₂ and y₁, y₂ and y₃ and between x₃and y₁, y₂, and y₃. Hence, y₁, y₂ and y₃ reconstruct unwanted (in thisexample) zeroth order beams 210' comprising x₂ ', and x₃ ', which takeconsiderable efficiency from the reconstruction of y₁ ', y₂ ', and y₃ '.

In the case of coherent and simultaneous recording of theinterconnection gratings, not only is fan-in throughput loss observed,but also coherent recording-induced crosstalk is seen. In FIG. 10' thetotal efficiency is, like in FIG. 9, considerably less than 1, due tothe beam degeneracy throughput loss. Further, the correct ratio of thefan-out is lost at and near the peak diffraction efficiency, due torecording-induced crosstalk. The notion of maintaining efficientinterconnections in such an arrangement is thus seen to be a myth.

FIG. 11 is similar to that of FIG. 8, except that it is based onemploying the architecture of the invention, and shows the angularmultiplexing of both the object (source) and reference beam sets 11, 13,respectively, as well as angular multiplexing of the fan-in to a givenoutput node. In FIG. 11, coherent pairs of object beams 11 and referencebeams 13 are depicted in like manner; since all of the reference beamsare mutually incoherent due to the source array 14 (as shown, forexample, in FIG. 6A), each reference beam x_(j) interferes with only onegiven object beam passing through the point y₁ ; therefore, none of thereconstructed beams 10' and zeroth order beams 210' are Bragg-matched toadditional gratings and hence no beam degeneracy throughput loss isobserved.

Coherent recording-induced crosstalk is eliminated among the referencebeams, since they are all mutually incoherent. Coherentrecording-induced crosstalk among the object beams is limited again bythe mutual incoherence of the source-derived beams to occur only amongthe set of object pixels illuminated by each coherent and expandedobject beam. This latter source of crosstalk is of lesser consequence inthe architecture of the invention, since all of the crosstalk terms tendto cancel out because of the type of mutual coherence involved in thereconstruction.

In FIG. 11, an incoherent fan-in due to output point y₁, is shown toconsist of a weighted sum of inputs of the form w₁₁ x₁ +w₁₂ x₂ +w₁₃ x₃=y₁ ', or, in general for an N-input, N-output fully connectedinterconnection network: ##EQU1##

The representation used for drawing the vector directions and scales ofthe input and output beams in FIG. 11 presumes an asymmetric input andoutput lens configuration (not shown). (Such an asymmetric input andoutput lens configuration is depicted in FIGS. 6A (lens 26) and 6B (lens38)).

5. Spatial Light Modulators

The detection, amplification, functional implementation, and modulationfunctions required in both the neuron unit output and input planes areenvisioned to be incorporated in multifunction spatial light modulators.A dual rail differential approach may be employed as it inherentlyincorporates considerable functional generality, with capacity toaccommodate both bipolar inputs and bipolar outputs. The simpler case ofunipolar outputs and bipolar inputs, also common in neural networkmodels, represents a subset of our fully bipolar design and requireseven less chip area. The dual rail approach involves the hybrid ormonolithic integration of two detectors, appropriate amplification andcontrol circuitry, and two modulators within each SLM pixel, as shown inFIGS. 12 and 12A. A primary approach is to develop analog circuitry thatis process-compatible with both detector and modulator requirements, andat the same time utilizes minimum integrated circuit real estate.Although development of second generation chips in the compoundsemiconductor system may utilize either multiple single-quantum-well ormultiple coupled-double-quantum-well modulation and detection elementsin conjunction with electronic circuit elements such as bipolar junctiontransistors, MESFETs, MISFETs, HEMTs or resonant tunnel diodes (RTDs),the first generation chips have been designed within the siliconrepertoire (MOSIS (Metal Oxide Semiconductor Implementation Service,Information Sciences Institute, University of Southern California)design rules) in order to establish functional integrity and preliminaryestimates of non-ideality and process-induced variances. Furthermore,hybrid integration of silicon chips (with integrated detectors andcontrol electronics) with compound semiconductor based or othertechnological implementations of the modulation function can beaccomplished by bump contact bonding in conjunction with appropriatethrough-substrate vias. Alternatively, the vias can be eliminated by theuse of transparent modulator substrates, with the modulation elementsoperated in the reflection mode, in conjunction with asecond-bump-contact-bonded substrate hybrid-integrated with the first toprovide the detection and control circuitry on the two innermost facingsubstrate surfaces. The current chip set contains 100×100 μm pixels,within which 2500 μm² is dedicated to dual rail circuitry thatimplements a linear transfer characteristic with both upper and lowerlevel saturation (FIG. 13), a function of considerable utility in theneural network application, as described in more detail in a succeedingsection. The design described herein incorporates only fifteentransistors per pixel within 2 μm minimum feature size design rules, andallows for 10⁴ dual rail pixels/cm².

While any of a variety of SLMs may be used in the practice of theinvention, a novel SLM described below is preferred. The preferred SLMis optically addressed (as opposed to electrically addressed) and isdepicted in FIGS. 12 and 12A. The SLM comprises a substrate 56comprising a plurality of pixels 58, at least two portions of each pixelcomprising regions 60 that can be controllably made transparent toincident light with varying degrees of optical density from a firstsource (such as source array 14). Means 62 are associated with eachtransparent region 60 to modulate the passage of light therethrough.Alternative means can be provided for modulation of the reflection oflight from, rather than the passage of light through, each separatemodulation element within each pixel.

Detector means 64 associated with each pixel detect incident light froma second source or set of second sources, such as from the output of themultiplexed storage hologram 20; see, e.g., FIG. 14. The detector meansgenerates an electrical signal, which is fed to electronic means 66associated with each pixel 58. The electronic means 66 is responsive tothe electrical signal from the detector and generates a modulationsignal which is sent to the modulation means 62. The electronic means 66comprises, therefore, the several functions of electrical signaltransduction (following each detector), signal amplification and levelshifting, transfer function implementation (establishment of thefunctional relationship between the input optical intensity and theoutput optical amplitude or intensity following the modulator element),and impedance matching to the electrically activated means of eachmodulation element. As a result, light transmitted through or reflectedfrom the SLM is modulated according to an overall transfer functionrelationship that implements a desired algorithmic dependence, asspecified further in the several following sections.

Both ⊕ (positive) and ⊖ (negative) channels are depicted in FIG. 12A.Note that both polarity channels are provided for each of the detectionand modulation functions within each individual pixel. In the preferredembodiment, this allows for the incorporation of both positive valuedand negative valued interconnection weights w_(ij), each carried as aseparate channel within each individual pixel. This arrangement may besummarized as allowing for the incorporation of both bipolar inputs andbipolar outputs within a given interconnection network.

In the preferred embodiment, the electronic means 66 is utilized in amodified differential amplifier configuration, which is designed suchthat the ⊕ modulator is driven to increasing transmissivity (orreflectivity) when the ⊕ detector output exceeds the e detector output;conversely, the ⊖ modulator is driven to increasing transmissivity (orreflectivity) when the ⊖ detector exceeds the ⊕ detector output.Additionally the ⊕ modulator is not driven when the detector outputdifference (⊕-⊖) is negative, and the ⊖ modulator is not driven on whenthe detector output differences is positive, as shown in FIG. 13.

Four additional novel spatial light modulator configurations are a partof this invention. In the first, the control circuitry is designed toimplement either an astable multivibrator or ring oscillator, witheither design-induced or process-variable-induced variance across thepixelated array in the center resonant frequency of the resultantoscillation, in such a manner that the individual pixels temporallymodulate fully coherent light producing a mutually incoherent set ofmodulated beams. Such a spatial light modulator configuration is onepreferred embodiment for the source array device described above. In thesecond, local interconnections among nearest neighbor ornext-nearest-neighbor pixels are incorporated such that the controlcircuitry drives the modulation elements in a manner that depends notonly on the one or more optical inputs to a given pixel, but also oneither the one or more optical inputs to neighboring pixels, or on somefunctional derivative thereof as determined by control circuitry in eachpixel. In the third, the modulation elements are designed in conjunctionwith a transparent substrate, or in the case of a hybrid integrateddevice with two transparent nonidentical substrates, such that themodulation creates a variable reflectivity and a variable transmissivityin each pixel, the one being the complement of the other in order tosatisfy conservation of energy laws. In this case, both the array ofreflected beams and the array of transmitted beams as so modulatedconstitute separate signals to be utilized in the implementation ofsystem functionality. In the fourth, two superimposed optical modulationelements are incorporated in each pixel, one vertically above the otheras referenced to the substrate plane, such that each is independentlycontrollable by means of the incorporated control circuitry (in turndependent on the electrical and/or optical input state(s) of eachpixel), with one of these elements exhibiting principally phasemodulation in response to its input variable, while the other of theseelements exhibits principally amplitude modulation in response to itsindependent input variable. In this manner, independent control of boththe amplitude and phase modulation exhibited by each pixel isachievable; in addition, compensation can be provided for undesirablemodulation-dependent phase in an amplitude modulation application, andthe compensation of undesirable modulation-dependent amplitude in aphase modulation application.

6. Holographic Recording Media

A wide variety of volume holographic recording media may be employed inthe practice of the invention, including static (fixed) media such asphotographic film, dichromated gelatin, layered thin film media, andcertain photopolymers, as well as dynamic (real time) media such asphotorefractive refractory oxide single crystals (e.g., bismuth siliconoxide, bismuth germanium oxide, bismuth titanium oxide, barium titanate,potassium tantalate niobate, strontium barium niobate, potassiumniobate, lithium niobate, and lithium tantalate), photorefractivecompound semiconductor single crystals (e.g., chromium-doped galliumarsenide, intrinsic (undoped) gallium arsenide, cadmium telluride, andiron-doped indium phosphide), photochromic glasses, andbiologically-derived photosensitive molecules dispersed in variousmatrices.

In each case, it is desirable for purposes of scalability in thepractice of the invention that such materials be configured so as toexhibit "thickν holographic grating characteristics, as defined by thewell-known holographic parameter Q defined by

    pi Q=2πλd/n√.sup.2

in which both λ and d have been previously defined, n is the average(unmodulated) index of refraction of the holographic recording medium,and √ is the period of a given recorded grating. Thick holographicgrating performance is usually observed when the recordingconfigurational parameters are so chosen or constructed that Q≧10. Forsuch values of Q, the Bragg width (angular response characteristicsabout the Bragg angle) given by Θ_(B) =arcsin(λ/2√) can be made narrowenough to support a large number of independent gratings capable ofreconstruction without interference, overlap, or interchannel crosstalk.

B. NEURAL NETWORKS 1. Technical Approach

The basic elements and functions of common neural networks are discussedabove and shown in FIGS. 1-3. A neural network typically learns bychanging its interconnection weights according to a learning technique,which is typically expressed as an update rule for the weights. Afterthe network has learned, the values of the interconnection weights maynot be known (and may be difficult to probe); only the correctperformance of the overall neural network is verified.

A general neural network architecture should have the followingfeatures: (1) modularity, i.e., be in the form of a cascadable "module";(2) capability for lateral, feedforward, and feedback interconnections;(3) analog weighted interconnections; (4) bipolar signals and weights;(5) scalability to large numbers of neuron units with high connectivity;and (6) generalizability to different network models and learningalgorithms, as well as capability for extension to possible futurenetwork models.

Recently, there has been a substantial amount of research anddevelopment on optical and optoelectronic implementations of neuralnetworks; to the best of the inventors' knowledge, none of the opticalor optoelectronic systems described to date by others havesimultaneously demonstrated all of the foregoing features. The apparatusdescribed herein, as applied to neural networks in the givenembodiments, provides for essentially all of the above features.

This architecture utilizes the novel incoherent/coherent hologramrecording and reconstruction apparatus of the invention, and has angularmultiplexing at each input node, configured to produce angularmultiplexing of the fan-in to a given output node. This provides forsimultaneous read/write capability with reduced crosstalk and enhancedoptical throughput. The use of this apparatus with multiplexed volumeholograms permits scalability of the neural network and itsinterconnections. It also provides simultaneous updates of all weightsat each iteration of learning. Since some learning techniques (e.g.,multilayer supervised learning) can require an extremely large number ofiterations for large networks, fast weight updating is crucial. Inaddition, since the copying apparatus described previously above can beused directly in neural network applications, rapid copying of allrecorded weighted interconnections can be readily performed. Thus,duplicates of a neural network that has learned a given processingfunction can be rapidly manufactured.

Optoelectronic spatial light modulators with hybrid or monolithicallyintegrated detectors, modulators, and electronics at each pixel asdescribed in the previous section are envisioned for the 2-D neuron unitarrays. These spatial light modulators provide for flexible functionswithin a single technology, thus enabling generalizability to differentneural network models and learning algorithms. They also permit bipolarsignals and synaptic weights to be integrated into the systemarchitecture.

The use of photonic technology provides for high fan-in/fan-outcapability via optics as well as parallel input/output for incorporationinto larger heterogeneous or homogeneous systems without loss of systemthroughput, thus providing modularity. Unlike current opticalarchitectures, the photonic architectures comprising preferredembodiments of the invention readily generalize to many neural networkmodels (including single and multi-layer, feed-forward and recurrentnetworks) and learning algorithms (supervised and unsupervised), withapplications to associative emory, combinatorial optimization, andpattern recognition, including vision and speech.

2. Interconnections

For the purposes of the present discussion, consider the connectionsfrom a single neuron unit, including fan-out and synaptic weights, to berepresented by a single hologram. During learning, all holograms areupdated simultaneously in a photorefractive crystal or other suitablevolume holographic recording medium. This is done by using oneself-coherent beam pair for each recorded hologram, in theincoherent/coherent, with angularly multiplexed fan-in apparatus andmethod described earlier (e.g., FIG. 6A). Referring to FIG. 6A, the setof reference beam intensities x_(j) serves as the set of input signalsto the neural interconnections, and the set of signals A_(j) serves asthe set of training signals during learning. The holograms are thenreconstructed by the same set of reference beams, as shown in FIG. 6B.This results in the desired incoherent sum Σ_(j) w_(ij) x_(j) at eachpixel of the output array, in which w_(ij) is the stored interconnectionweight from neuron unit j to neuron unit i.

Experimental results on writing and reading angularly multiplexed volumeholograms using this incoherent/coherent process in silver halide andphotorefractive bismuth silicon oxide media show minimal crosstalk atthe same time as high optical throughput.

The advantages of this technique are as follows:

(1) All weights can be updated simultaneously. This obviates the needfor sequential exposures which are inefficient as well as timeconsuming, and at the same time maximizes parallelism.

(2) Both the object beams and the reference beams are angularlymultiplexed, and each training signal pixel as well as each output nodecorresponds to a set of angularly multiplexed beams. This circumventsthe problem of incoherent fan-in loss, maximizing optical throughput,providing incoherent pixel-by-pixel summation, and minimizing beamdegeneracy crosstalk. (In addition, crosstalk due to accidental gratingdegeneracies is eliminated by optimization of the geometry of the beams,as well as by the spatial light modulator placement and pixelation; see,e.g., D. Psaltis et al, Proc. SPIE, Vol. 963, pp. 70-76 (1988).)

(3) As described above, this technique permits the capability of rapidlycopying the entire collection of recorded interconnections and weightsto another volume medium by using this same incoherent/coherentreconstructing and recording technique. In addition to that describedabove, another advantage of this technique is the capability to refreshthe interconnection periodically, by copying it back and forth betweentwo or more holographic media; additionally, two parallel networks canbe implemented to separate the learning function from the processingfunction. The architecture described herein is unique to the best of theinventors' knowledge in allowing for this possibility.

In order to adaptively interconnect a large number (10⁴ to 10⁶) of inputelements to an equally large number of output elements with highconnectivity and negligible crosstalk, the most attractive candidatetechnology is currently that of photorefractive volume holographicoptical elements. For many (if not all) proposed optical implementationsof neural networks, including that described herein, demonstration ofappropriate degrees of reconfigurable multiplexing capacity withnegligible or at least tolerable interconnection crosstalk is essentialto the achievement of successful integration. The architecture proposedherein is uniquely designed to accentuate the strengths of currentlyavailable photorefractive materials (such as Bi₁₂ SiO₂₀ and GaAs), whileminimizing the inherent weaknesses. For example, the incorporation of afully parallel weight-update scheme with mutual incoherence betweenpairs of sources results in a significant reduction in the degree ofsource-generated crosstalk characteristic of fully coherent recordingschemes, while simultaneously obviating the need for sequentialrecording that is particularly cumbersome and time consuming inphotorefractive media.

3. Learning Techniques.

A broad class of learning techniques, both supervised and unsupervised,can be represented by the single weight update equation:

    Δw.sub.ij =αδ.sub.1 x.sub.j -βw.sub.ij (1)

in which Δw_(ij) =w_(ij) (k+1)-w_(ij) (k) is the weight update, x_(j) isthe signal level of the j^(th) input e.g., j^(th) neuron unit of theprevious layer in a multilayer network), and δ₁ is dependent on theparticular learning technique. In Eqn. (1) above, α>0 is required andβ≧0 is dictated by the physical constraints of the material. Thearchitectures described herein implement learning of the form of Eqn.(1). Specific examples include: ##EQU2## in which y_(i) denotes theoutput of neuron unit in the current layer, t₁ is the target or desiredvalue for the output of neuron unit i for supervised learning, δ₁,l isthe error term of neuron unit i in the l^(th) layer, and f(p₁,l)represents the neuron threshold function of the neuron potential p₁,l ofthe i^(th) neuron in the l^(th) layer. The index represents the outputlayer, and B are constants. In particular, α is the learning gainconstant and β is the decay constant. The last term is an optional decayterm that is included primarily to model intentional or unintentionaldecay of gratings in a photorefractive crystal. Other important physicaleffects include non-linearities in the response of the medium. Forexample, with appropriate encoding of data, the photorefractive materialcan yield a network response of Δw_(ij) αsgn(δ₁ x_(j))(|δ₁ x_(j)|)^(1/2), in which sgn(u) is equal to +1 if u>0, -1 if u< 0, and 0 ifu=0. Simulations indicate that such a non-linearity can actually improvethe performance of the apparatus during learning. (Most other physicaleffects such as saturation and non-uniformities in the medium areconsidered primarily unintentional and can be treated or accounted forseparately.)

Thus, the implementation problem reduces to (1) implementing the weightupdates given in the generic learning technique of Eqn. (1), and (2)generating the terms δ for the appropriate learning technique. Theformer is the more difficult task, and once it is accomplished, manylearning techniques, the above comprising only a few examples, can beimplemented.

4. Neuron Units and Weight Update Calculation

Two-dimensional optoelectronic spatial light modulator (SLM) arrays,with integrated detectors, modulators and electronics, as shown in FIG.15, are envisioned for conventional inner product neuron units, as wellas for generation of the δ₁ terms. This technology provides: (1)incorporation of bipolar signals via two-channel inputs and outputs; (2)slight variants of the same basic SLM structure for all SLMs in thearchitecture (for neuron units and δ₁ generation): (3) incorporation ofdifferent neuron unit functions, including linear, soft threshold, andhardclipping, as well as variable gain; and (4) potential extendabilityto future neural network models.

5. Architecture

The architecture for the case of Hebbian learning, δ₁ =y_(i), wherey_(i) is the output of neuron unit i, is shown in FIG. 14.(Generalization to other learning techniques is given below.) Onlyfeedforward connections are shown.

The two sets of recording beams 11 and 13 and the components therein arethe same as described in FIG. 6A. Modulator 32 (x_(j)) serves as theinputs to the interconnections; the write-input 70 of modulator 32(x_(j)) is the input to the neural network; alternatively, this inputcan be derived from the previous layer or module. The output(reconstructed) hologram beams 10' reflect off mirror 72, and are imagedvia lens 74 onto the write side of spatial light modulator 28, afterreflecting from beamsplitter 76. Lens 74 in effect images the output ofSLM 28 (virtual image), through recording medium 20, and onto the inputof SLM 28. The combination of detector(s), control electronics, andmodulator(s) that comprise SLM 28 is used to form the array of neuronoutputs y_(i), which are functionally dependent (e.g., by means of athreshold or sigmoid response) on the incoherent weighted sums of theform Σ w_(ij) x_(j) summed over j.

Dove prism 78 serves to flip the beam so that the image orientation atSLM 28 is consistent. Then, the readout beam passing through SLM 28 haspointwise intensity proportional to y_(i), the output of the neuronunits as determined by the weighted interconnections in the layer ormodule depicted in FIG. 14. Output beam 110" is directed to a subsequentmodule or layer, or can be used to generate outputs of the neuralnetwork. Lateral and feedback interconnections are implemented by addingan optical path similar to the output path 10', in this case byincorporating a beamsplitter behind medium 20, and reflecting a portionof the set of output beams 10' around the bottom of FIG. 14, to beimaged onto the input side of SLM 32. This provides lateral and feedbackconnections within medium 20. If fixed connections are desired (as isoften the case for lateral connections), while maintaining adaptivefeedforward connections, then instead a path is inserted from behindlens 36 (via a beamsplitter), through a separate hologram, and is imagedonto the input side of SLM 32. The same optical arrangement is also usedwhen adaptive lateral and/or feedback connections that update by adifferent training technique than the feedforward connections aredesired.

During the computation phase, the shutter 24 is closed to preventlearning. The array of sources is imaged onto SLM 32 as a set of readbeams. Each beam is modulated by SLM 32 to provide the inputs. Then each(reference) beam x_(j) passes through the hologram 20 to provide theinterconnections, i.e., the weighted fan-out from each input x_(j). Thehologram output is sent to the write side of SLM 28 via the lens 74, atwhich point the pointwise incoherent sums are detected, functionallytransformed, and used as inputs to the modulator(s) within eachindividual pixel.

In the learning phase, the shutter 24 is open. The weight update term iscomputed optically (by the spatial modulation of beam 11 SLM 28 and bythe pairwise interference of the object and reference beams) andrecorded into the photorefractive material 20. Light from each source isapproximately collimated and used as the read beam for SLM 28. Thus, foran N by N array of sources, there are N² beams reading SLM 28simultaneously, each at a different angle; all y_(i) terms are encodedonto each of these beams. Each of these beams interferes only with itscorresponding reference beam, x_(j), from the same source, in thephotorefractive material 20. This writes the set of desired weightupdate terms αx_(j) y_(i).

A generalized architecture is shown in FIG. 15. The paths and componentsfor recording the holograms are the same as above, except for thetraining term generator 80 and an additional shutter 81. The purpose ofgenerator 80 is to optically generate the δ_(i) terms according to thelearning technique being implemented. In general, there are as many asthree different input signals to generator 80 (usually at most two ofthem are needed for a given learning technique). The input t_(i) on beam82 is a target or desired output signal for supervised learning, y_(i)are outputs (and p_(i) are the corresponding potentials) of neuron unitsat the output of the current module. Beams 110" write onto spatial lightmodulator 84 (in an image plane of the exit plane of generator 80); theSLM is then read out by beam 10", through lens 86 which images SLM 84onto the appropriate SLM in the generator.

Means for implementing sample learning techniques (for generator 80) areshown in FIG. 16. These implement the well-known (A) Widrow-Hoff, (B)Perceptron, and (C) least mean square (LMS) learning techniques. Allspatial light modulators have differential (positive and negativechannel) inputs and dual channel outputs (both positive and negative).They all have nearly the same circuitry. Spatial light modulator 88provides a linear difference of the inputs; spatial light modulator 90has a higher gain with saturation to provide a binary response; spatiallight modulator 92 provides a non-monotonic function (e.g., Gaussian)for the f'(p_(i)) term. Spatial light modulator 32 in other figures isthe same as SLM 88, except for a soft thresholding characteristicprovided by the control circuitry and output drivers in SLM 32. For thecase of back propagation (LMS) in a hidden layer, the pair of signalsy_(i) and t_(i) input to each pixel in (C) is replaced by the error termΣ_(k) δ_(k),l w_(ki) from the previous layer. Each layer generates sucherror terms in the following manner. Beam path 11 passes through thehologram 20 and reconstructs an additional output beam. This additionaloutput beam contains the information Σ_(k) δ_(k),l w_(ki) and is sent tomodulator 88 of the previous layer. It should also be noted that analternative arrangement can implement multilayer neural networks in asingle module of FIG. 15, by directing the output signals 110" to theinput of SLM 32, using optical feedback to enable multiple passesthrough different neuron units and through the same holographic medium20.

A variant of this architecture can be obtained by exchanging the spatiallight modulators 28 and 32, as shown schematically in FIG. 17. (SLM 28is again replaced by SLM 80 for the general case.) In this case, theupper SLM 32 in FIG. 17 represents the layer inputs x_(j), while thelower SLM 28 represents y_(i). The optical feedback is imaged onto thelower SLM 28. This provides for coherent fan-in at each neuron unitinput. With intensity coding of data, this coherent sum deviates fromneural models, but in some cases may provide an increase in diffractionefficiency to each neuron unit.

In the preferred embodiment, the object SLM 28 performs spatial(parallel) modulation of the object beams, while SLM 32 performsindependent modulation of each reference beam. In the variant describedabove, SLM 32 performs spatial (parallel) modulation of each referencebeam, while SLM 28 performs independent modulation of each object beam.In two additional configurations, both SLMs may perform spatialmodulation, or both SLMs may perform independent modulation. Specificapplications will dictate the particular choice of modulation.

C. TELECOMMUNICATIONS

Photonic switching networks may be divided into two categories:telecommunications switching and interconnection networks for digitalcomputing. The primary difference between these two categories is in thedistance scale and the data bandwidth per channel required by theapplication; as a result, telecommunications data channels are typicallycarried on optical fibers and have many multiplexed data channels oneach fiber, with wavelength division multiplexing being a commonmultiplexing technique. Interconnection networks for digital computing(1) may have data channels on optical fibers or on free-space opticalbeams, (2) can be much higher bandwidth per channel, and (3) usually donot multiplex more than a few channels on one optical signal line. Localarea networks are in between these two realms, and are not discussedhere, as once the two more extreme cases are illustrated, the middleground is a straightforward extension.

In this section, embodiments of the invention are described for theapplication of telecommunication switching networks. It is assumed thatthe input and output optical signals are wavelength divisionmultiplexed, although the embodiments are applicable to a broad range ofchannel multiplexing schemes. The embodiments described are directlyapplicable to circuit switching networks. In this case, it is importantto distinguish between the control signals that are used to set theroutes and state of the switch, and the (high bandwidth) data signalsthat are routed through the switch from an input or source node to anoutput or destination node. In addition, one physical input datatransmission line (i.e., one optical fiber) is referred to herein as adata line, and each individual information channel as a data channel.Thus, many data channels, each at a different optical wavelength, aremultiplexed onto one data line. An array of data lines is input to andoutput from the optical switch.

Photonic switching networks should have the following properties: (1)high bandwidth for the data signals, (2) compatible physicalinterface(s) to the optical input and output lines, (3) compatibilitywith multiplexing schemes utilized for the input and output lines(usually by demultiplexing the input signals and re-multiplexing theoutput signals), (4) capability for implementing a large number of inputand output lines in a relatively compact package, (5) packet and/orcircuit switched control, (6) reconfigurability at a low-to-moderaterate (for circuit switched networks) or at a high rate (for packetswitched networks), and (7) ability to re-route some data signals whileother data channels are being used. In addition, it is desirable to havethe capability for broadcast (fan-out) of a data channel in someapplications, as well as fan-out and fan-in of a physical data line.

The first described embodiment will accommodate a 1-D array ofwavelength division multiplexed (WDM) inputs and a 1-D array of WDMoutputs. The apparatus is shown in FIG. 18. A source array means isprovided at 214; this consists of a two-dimensional array of sources,each at a different center optical frequency ν_(j) along one dimension(e.g., row), with each individual source along the other dimension(e.g., column), all at essentially the same center frequency, butarranged so as to be mutually incoherent, as in previously discussedembodiments. Each center frequency ν_(j) corresponds to the centerfrequency of one optical data channel. Two means for providing thisarray are described below. This source array provides illumination forthe control signals. The set of optical beams from 214 are split bybeamsplitter 16. The reference beams are reflected from 16, pass thoughshutter 81, through optics 130 and are additionally reflected fromreflecting means 22. The optics 130 are anamorphic and serve to condensethe dimension of different center frequencies to a single pixel at 132,while imaging the dimension of mutually incoherent sources centered atν_(j) from 214 to source control 132. At 132, means are provided formodulating each pixel independently, and for making the phase frontsleaving 132 substantially identical to the phase fronts leavingwavelength demultiplexer 94. If the modulator in 132 has a high enoughcontrast ratio and turns off sufficiently well, then shutter 81 is notneeded. The beams leaving 132 are made to pass through beamsplitter 96and optics 136 that very approximately collimates the beams. In the caseof focal lengths and distances being appropriately chosen, optical means136 can be omitted. The beams are then incident on volume holographicrecording medium 20. The source array as modified and passed throughcontrol element 132 provides the set of reference beam illuminationsignals for the holographic recording process. The other set of beamsfrom source array 214 passes through beamsplitter 16, shutter 24, optics126, and destination control 128 which consists of a spatial lightmodulator that serves to input the routing function. The beams are thenincident on the holographic recording medium 20. Optics 126 areanamorphic and serve to image the beam in the dimension of the differentoptical center frequencies ν_(j) from the source array 214 to themodulator 128. In the dimension of mutually incoherent sources centeredat ν_(j), optics 126 serves to direct the beam from each source throughall corresponding pixels of 128 in the corresponding 1-D dimension(e.g., column). This completes the control signal portion of theapparatus.

A set of switch states can be loaded into the hologram by any of threetechniques: (1) sequencing through the one-dimensional array of pixels132 one at a time, interfering each with appropriate destination controlsignals from 128 (thus recording control signals for all wavelengths ofa given input line in one step); (2) sequencing through a set of updatesgiven by the interference of many pixels in 132 with pixels in 128,similar to the neural network case described above; or (3) a compromisebetween these two extreme cases. A potential advantage of (2) is adecrease in the number of sequences required in certain cases.

The data signals input to the switch and arranged in plane 98 (e.g.,from optical fibers 99), are sent through an optical wavelengthdemultiplexer 94 (e.g., a grating), reflect off beamsplitter 96 andfollow a substantially identical path from 96 to the holographicrecording medium 20. The exit plane of 94 is in a conjugate (image)plane of the exit plane of 132. When the two sets of control beams from214 are blocked (via shutters or modulator means in 132 and 128), onlythe data signals pass through the holographic medium. After diffractingfrom the recorded interference patterns in medium 20, the output datasignal beam passes through optics 174, 174' to plane 310, which is animage plane of the modulator 128. Then, fiber interface unit 312, whichconsists of optics and an optical wavelength multiplexer, multiplexesall wavelengths along the optical center frequency ν_(j) dimension, inorder to yield the one dimensional wavelength division multiplexedoutput at data output plane 314. An optical fiber array 315, forexample, can be arranged following 314 to receive the re-routed andre-multiplexed data signals from the data inputs arranged at 98, theserouting and multiplexing functions can include channel broadcast, linebroadcast, and line fan-in functions.

Once established, the routes through the switch can be changed all atonce by erasing the holographic recording material and then re-recordingthe new interconnection pattern. Individual routes can selectively bechanged by either of two techniques: (1) not refreshing the old routesto be changed, which will then decay in time, and refreshing the newroutes; or (2) erasing specific gratings using binary phase modulationin 128 and 132; such phase modulation to selectively erase gratings hasbeen previously demonstrated; see, e.g., A. Marrakchi, Optics Letters,Vol. 14, No. 6, pp. 326-328 (Mar. 15, 1989).

Two alternative means for providing the source array 214 are describedherein. In FIG. 19A, a two-dimensional array of sources 316 is shown, inwhich the center optical frequency is varied along dimension 318, andthe mutual incoherence of the sources with essentially the same centerfrequency is provided along dimension 320. This can be accomplished, forexample, by providing an array that is designed to implement thewavelength variation in one dimension of the array, with typicalprocessing-induced stochastic variation providing the required mutualincoherence in the second dimension. This array can then be useddirectly in plane 214.

Another means for providing the source array distribution 214 is shownin FIG. 19B. In this case, two one-dimensional arrays are used. Element322 is a one dimensional array of sources, e.g. laser diodes, each witha different optical center frequency ν_(j), and can be fabricated as aone-dimensional version of source array 316. Optics 324 expands thebeams in the dimension perpendicular to 322, and condenses in thedimension of source array 322 before passing through one-dimensionalphase modulator 326. Each pixel of modulator 326 provides phasemodulation at a different frequency, and can be fabricated as aone-dimensional version of the pixelated piezoelectric mirror or purephase modulator array described previously in Section A2. Optics 328then expands the result in the orthogonal dimension, thereby producing atwo-dimensional array, which can then be used as the input source array214. The optics 324 and 328 in FIG. 19B are essentially the same asthose of an analog optical outer product matrix processor (R. A. Athale,Proceedings Tenth International Optical Computing Conference, IEEECatalog No. 83CH1880-4 pp. 24-31, April 1983). It will be noted that inthis case, the beamsplitter 16 can be inserted before the plane S_(i)(but after 326); this will make the overall system more compact.

Referring now to the case of two-dimensional WDM data input lines andtwo-dimensional WDM data output lines, the apparatus is again shown inFIG. 18, but the following components have different functions thanthose described for the case of one-dimensional data signals. The sourcearray 214 is a two dimensional array, each element of which has adifferent frequency modulation imposed on it in order to produce mutualincoherence among all the source elements; each element of the sourcearray 214 which contains beams of all center frequencies ν_(j), whichcorrespond to the center frequencies of each data signal channel. Meansfor providing this are described below. In the case of applications thatdo not require data channels to fan in, and do not require output datachannels to be angularly multiplexed, the mutual incoherence is notrequired; only means for amplitude modulating individual elements arerequired. Optics 130 now image from 214 to the modulator plane in 132.The source control 132 consists of both an optical wavelengthdemultiplexer and a two-dimensional modulator. Optics 136 again veryapproximately collimates the beams. Optics 126 directs the light fromeach pixel of 214 through every pixel of the modulator in 128. Thedestination control now includes an optical demultiplexer (e.g.,grating). The data inputs at plane 98 are now arranged in atwo-dimensional array, as are the data outputs at plane 314. The opticsof 312 is now simpler than that required for the previously discussedembodiment, as all of the reconstructed pixels are imaged by 20 and 174,174' onto the correct locations for output at plane 310.

Means for providing the source array signals are shown in FIG. 20. A twodimensional source array (e.g., surface emitting laser diodes) 330provides an array of sources, each at a different center frequencyν_(j). The optics 332 directs the light from each source element to allpixels of the two-dimensional modulator array 334. Each pixel ofmodulator array 334 provides phase modulation at a different frequency,and can be fabricated as the pixelated piezoelectric mirror or purephase modulator array described in Section A2. Modulator array 334 thenprovides the optical signals of plane 214 as depicted in FIG. 18. Asdiscussed above, in the common case of applications that do not requiredata channels to fan in and do not require output data channels to beangularly multiplexed, the mutual incoherence is not required. In thiscase, modulator array 334 provides the requisite amplitude modulation.Furthermore, in most such applications, binary amplitude modulation issufficient. If optics 332 is provided by simple (non-multiplexed)elements, such as a simple beam expander (e.g., lens), then an opticalwavelength multiplexer 336 (e.g., set of gratings) is incorporated asshown. Its function is to fan in the beams of different centerfrequencies to be collinear at each pixel.

Finally, it should be noted that by more precisely collimating the beamsat the recording medium 20 and by choosing center frequencies ν_(j)appropriately, the apparatus described above can be extended to atwo-color system in which the data signals read out the storedholographic interconnections non-destructively. In this case, thegeometry and scaling of the optical data paths are changed relative tothose of the optical control signal paths.

D. DIGITAL COMPUTING

For the application of digital computing interconnections, it is assumedthat the inputs and outputs are not wavelength division multiplexed,such WDM cases having previously been discussed above. Further, they canbe input to, and output from, the interconnection network in the form ofoptical fibers or as free space beams that are imaged from one plane toanother. In the case of optical fibers, a photonic system for a crossbarinterconnection network can be explained using FIG. 18, in which thefollowing components are interpreted differently than in thetelecommunications application previously described. The data inputs andoutputs are arranged in 2-D arrays. The source array 214 is a 2-D arrayof individually coherent but mutually incoherent sources, as describedabove. Here they all have the same center wavelength. The remainingcomponents in FIG. 18 are the same as in the telecommunicationsswitching apparatus, for the case of 2-D data input and output arrays,with the exceptions detailed herein. Since the input and output data arenot wavelength multiplexed, the wavelength multiplexers anddemultiplexers in 94, 128, and 312 are not needed. The output fiberinterface unit 312 comprises only the optical element(s) needed tocouple the light into each fiber.

The control procedure for recording the interconnections is the same asin the telecommunications embodiment above, except that there is nowavelength dimension. Control can again be accomplished by making arecording for each single pixel of the SLM in 132, interfering withlight from all destination control pixels of SLM 128. Alternatively, allpixels of both SLMs can be used during each recording cycle, in effectsumming over a set of matrices of rank one to build up aninterconnection pattern, similar to the neural case.

An extension of this apparatus utilizing the copying technique describedherein enables faster computing. Two volume holographic recording mediaare employed. The primary holographic medium is used for the actualcomputation, and a secondary holographic medium is used to record theset of interconnection patterns from the control inputs. When therecording of a set of new interconnection patterns into the secondarymedium is completed, it is copied into the primary medium in a singlestep. In this way, computation is being performed while the next set ofinterconnections is being configured. While recording of a newinterconnection configuration can take some time, the copying can takeplace in one step. This minimizes the network reconfiguration time ofthe switch.

The same apparatus can be used for free space data inputs and outputs,by removing interface unit 312. Note that this is in effect ageneralized crossbar, in that it not only allows arbitrary 1-to-1interconnection, but also enables fan-out and fan-in. In addition, atwo-wavelength system can be employed, as in the two-colortelecommunication application, by changing the scaling and geometry ofthe optical data paths relative to the optical control signal paths.This enables non-destructive read-out.

E. HOLOGRAPHIC OPTICAL ELEMENTS

Holographic optical elements (HOEs) are elements that are used inoptical systems and may include such elements as multi-focal lengthlenses, specific combinations of wavelength dispersive andwavefront-modifying optical elements, and for purposes here, alsoholographic elements for display. Examples include, but are not limitedto, head-up displays (HUDs), dichroic beamsplitters,aberration-corrected lenses, multi-function beamsplitters, multiplefocal length lenses, and space-variant optical elements.

Advantages of HOEs over conventional optical elements include reducedsize, weight, and cost; additionally, in some cases, there are nopractical alternatives to certain HOEs. Furthermore, if the HOE can berapidly copied, then a large savings in production cost can be achieved.

A volume hologram can store a large amount of information; the processof recording all of the needed information into the volume can be asignificant bottleneck in both initial development and production. Inthe present application, two realms are discussed: (1) that of recordingcomplex fringe patterns in the holographic recording medium thatcorrespond to combinations of optical elements, so that the phase frontscan be generated relatively easily and recorded relatively quickly; and(2) a computer aided approach in which a series of exposures is cycledthrough in order to build up the requisite interference fringe patternin the holographic recording medium.

In the latter case, the input patterns used for each exposure aregenerally calculated by computer or neural network. However, if theinput patterns are known a pri-ori, and a suitable input device isavailable, no computations of the fringe pattern need be made. Anexample of this is a multiplexed holographic display in which eachhologram to be displayed consists of a page of information.

An example of the former case is depicted in FIG. 21. Two types of HOEsare discussed herein that can be generated from this apparatus. First,consider a HOE that functions as a space-variant lens, focusing incidentplane waves at different distances z, the distance depending on theincident angle of the plane wave. The array of sources 14 generates aset of coherent but mutually incoherent beams, which are split into twopaths. The upper path carries the reference beams in this case; they aretransmitted by beamsplitter 16 and pass through optics 226 to thehologram 20. The spatial light modulator 228 is not needed for theexposure of this particular HOE. Optics 226 essentially collimates eachbeam. For response to other than collimated beams, optical means 226 canbe changed to provide the appropriate focal power. The lower pathfunctions to carry the set of object beams.

After reflecting from beamsplitter 16, optics 230 approximately imagesthe source array 14 onto each pixel of modulator 232. In this case,modulator 232 is a static or dynamic planar microlens array. This arrayprovides a different and programmable focal power for each source beam.Optics 236 is used to convert the spherically expanding waves tospherically contracting waves, and to provide relay optics when needed.

Upon reconstruction, plane waves incident on the holographic medium atthe angles of the upper beam paths utilized during recording areconverted to spherically contracting waves of different focal lengths,thus providing a highly multiplexed lens with space-variant focallength.

In order to generate a space-variant lens capable of convertingspherically expanding waves to spherically contracting waves, theapparatus of FIG. 22 can be used. It is the same as the apparatus ofFIG. 21, except that in this case, the upper path passes through optics350, which approximately images the source array onto the modulator 228.Means are provided by modulator 228 to modulate each imaged element ofthe source array in focal power (e.g., by means of a dynamic microlensarray) to produce the desired space variant focal length HOE. Certainother applications require element 228 to modulate phase, or amplitudeand phase, instead of focal power.

Another mode of recording permits a larger aperture of holographicrecording medium 20 to be utilized for each point-spread functionresponse of a space-variant HOE; it uses the apparatus of FIG. 21. Thismode can be utilized to record essentially arbitrary phase fronts thathave values at each pixel between 0 and 2π. An example of such anoptical element is a multiplexed HOE that stores Fresnel lenses ofseveral different focal lengths; note that this can include sphericalFresnel lenses as well as anamorphic Fresnel-type lenses, and other evenless symmetric phase fronts. In this mode, the upper path carries theobject beams and the lower path carries the reference beams.

The modulator 228 is a spatial light modulator that modulates phase ateach pixel; modulator 232 is an amplitude spatial light modulator and isused to set the diffraction efficiencies of each recorded hologram.Optics means 236 is configured to produce a set of multiplexed referencebeams that are substantially identical to the anticipated collection ofreference beams to be utilized during reconstruction. During exposure,in one embodiment the sources in 14 are turned on one at a time, and thedesired object pattern is written onto modulator 228 for each source. Ifthe same pattern at modulator 228 is to be used for multiple sources(i.e., multiple holograms), then those sources pertaining to a commonobject pattern can be turned on simultaneously, reducing the requisitenumber of recording steps. Depending on the application, this can resultin considerable or even dramatic savings in recording time. In the fullysequential case, the described apparatus utilizing the two-dimensionalsource array still has the advantage of permitting recording of theentire multiplexed HOE without any moving parts.

For reconstruction, the HOE is illuminated with reference beamssubstantially identical to those used during exposure, except that theymay be independently and arbitrarily amplitude modulated. The outputbeams then give the desired phase front patterns according to the objectpatterns that were recorded. This provides a space-variant HOE in whichthe point-spread function response can be chosen essentiallyindependently for each pixel of an input array. For applicationsrequiring space-invariance over small local regions of the input plane,the same object pattern can be recorded for reference beamscorresponding to neighboring pixels in the input array, oralternatively, the hologram thickness is chosen appropriately and fewerrecording beams are used, yielding space-invariance within the Braggangle of a particular hologram.

According to the teachings of the invention, it will be appreciated thatseveral additional methods of multiplexing can be utilized to advantageduring the recording of holographic optical elements, including angular,spatial, and/or wavelength multiplexing of both the object and referencebeams.

It will also be noted that for certain appropriate applications, theupper path of the apparatus may be interpreted as carrying the referencebeams, and the lower path may be interpreted as carrying the objectbeams. Then, during reconstruction, when beams of appropriate phasefronts are incident on the holographic medium, the output beamsreconstruct spots in an image plane of optical means 232. Eachreconstructed spot then has a value proportional to the similarity ofthe incident wavefront to one of a set of stored basis functionwavefronts. (These basis function wavefronts are dependent on the inputpatterns during recording and the angle of each such reference beamduring recording.)

Finally, consider the case of a sequence of exposures, in which thedesired object patterns are not input directly, but rather are designedsuch that the resultant recorded holographic fringe pattern, at thetermination of the exposure sequence, produces upon reconstruction thedesired output functions. In this case, it is in general desirable tomodulate both the phase and amplitude of the incident beams, which canbe implemented with a spatial light modulator characterized byindependent control over both amplitude and phase in each individualpixel, as described above; however, it should be noted that a largeclass of patterns can be recorded with either phase modulation only, orwith amplitude modulation only. In this operational mode, the designedset of object patterns can be produced either by computer aided designtechniques (for cases in which the desired holographic recording patternis either known or can be computed with reasonable resources), or by aneural-like learning rule in which a sequence of weight updates areproduced in response to a set of training patterns. In the latter case,supervised learning algorithms are exploited when desired outputpatterns can be represented, and unsupervised learning algorithms areexploited otherwise. The neural technique permits the HOE to converge toan approximate version of the desired HOE, without knowledge of thestored fringe pattern within the holographic medium.

INDUSTRIAL APPLICABILITY

The present invention is expected to find use in neural networks,telecommunications, digital computers, and holographic optical elements.

What is claimed is:
 1. Apparatus for providing multiplexed volumeholographic recording comprising:(a) means for providing an array ofcoherent light sources that are mutually incoherent; (b) means forsimultaneously forming an object beam and a reference beam from eachcoherent light source, thereby forming a set of multiplexed object beamsand a separate set of multiplexed reference beams; (c) means formodulating each object beam; (d) means for modulating each referencebeam; (e) a holographic medium capable of simultaneously recordingtherein a holographic interference pattern produced by at least aportion of set of all modulated multiplexed object beams and of said setof all modulated multiplexed reference beams pairwise, all such pairsbeing mutually incoherent with respect to one another; and (f) means fordirecting at least a portion of said set of modulated object beams andof said set of modulated reference beams onto said holographic mediumand for interfering said portion of said set of modulated object beamsand of said set of modulated reference beams, pairwise, inside saidholographic medium.
 2. The apparatus of claim 1 wherein said array ofcoherent light sources comprises a two-dimensional array of saidsources.
 3. The apparatus of claim 1 wherein said array of coherentlight sources comprises an array of semiconductor laser diodes, eachlaser itself coherent, and each laser operating at a slightly differentfrequency than the other lasers.
 4. The apparatus of claim 1 whereineach said set of multiplexed object beams and each said set ofmultiplexed reference beams is independently multiplexed in at least oneof angle, space, and wavelength.
 5. The apparatus of claim 4 in whicheach object beam of a pair is at a separate, first given angle, and itsassociated mutually coherent reference beam is at a separate, secondgiven angle.
 6. The apparatus of claim 1 wherein each object beam isspatially modulated so that all object beams are identically modulatedand each reference beam is independently modulated.
 7. The apparatus ofclaim 1 wherein each object beam is spatially modulated so that allobject beams are identically modulated and each reference beam isspatially modulated so that all reference beams are identicallymodulated.
 8. The apparatus of claim 1 wherein each object beam isindependently modulated and each reference beam is spatially modulatedso that all reference beams are identically modulated.
 9. The apparatusof claim 1 wherein each object beam is independently modulated and eachreference beam is independently modulated.
 10. The apparatus of claim 1wherein at least one of said means for modulating said object beam andsaid means for modulating said reference beam comprises a spatial lightmodulator.
 11. The apparatus of claim 10 wherein said spatial lightmodulator comprises an array of integrated optical detectors, opticalmodulators, and electronics, said detectors capable of detecting atleast one control beam incident thereon to generate a detected signal,said electronics capable of processing said detected signal andcontrolling the amount of modulation of said modulators, and saidmodulators capable of modulating one of said sets of beams.
 12. Theapparatus of claim 1 further including means for selecting at least aportion of said set of modulated object beams and of said set ofmodulated reference beams, said portion of said sets selected prior toforming said interference pattern.
 13. The apparatus of claim 12 whereinsaid selecting means is provided by independent control of said coherentsources of said array.
 14. The apparatus of claim 1 wherein saidholographic medium comprises a photorefractive material capable ofreal-time recording and reconstruction of holographic images. 15.Apparatus for providing multiplexed volume holographic recordingcomprising:(a) means for providing an array of coherent light sourcesthat are mutually incoherent, said array of coherent light sourcescomprising an array of semiconductor laser diodes, each laser itselfcoherent, and the individual lasers mutually incoherent; (b) means forforming an object beam and a reference beam from each coherent lightsource, thereby forming a set of angularly multiplexed object beams anda separate set of angularly multiplexed reference beams; (c) means forspatially modulating each object beam so that all object beams areidentically modulated, said means comprising a first spatial lightmodulator; (d) means for independently modulating each reference beam,said means comprising a second spatial light modulator; (d) aholographic medium capable of simultaneously recording therein aholographic interference pattern produced by at least a portion of saidset of all modulated object beams and of said set of all modulatedreference beams pairwise, each object beam of a pair at a separate,first given angle, and its associated mutually coherent reference beamat a separate, second given angle, all such pairs being mutuallyincoherent with respect to one another; and (f) means for directing atleast a selected portion of said set of modulated object beams and ofsaid set of modulated reference beams onto said holographic medium andfor interfering said portion of said set of modulated object beams andof said set of modulated reference beams, pairwise, inside saidholographic medium.
 16. The apparatus of claim 15 wherein saidholographic medium comprises a photorefractive material capable ofreal-time recording and reconstruction of holographic images.
 17. Theapparatus of claim 15 wherein at least one of transmittance andreflectance of the modulator of each pixel of said spatial lightmodulator is encoded onto said set of angularly multiplexed objectbeams.
 18. The apparatus of claim 15 further including means forselecting at least a portion of said set of modulated object beams andof said set of modulated reference beams, said portions of said setsselected prior to forming said interference pattern.
 19. Apparatus forproviding multiplexed volume holographic recording and readoutcomprising:(a) means for providing an array of coherent light sourcesthat are mutually incoherent; (b) means for simultaneously forming anobject beam and a reference beam from each coherent light source,thereby forming a set of multiplexed object beams and a separate set ofmultiplexed reference beams; (c) means for modulating each object beam;(d) means for modulating each reference beam; (e) a holographic mediumcapable of simultaneously recording therein a holographic interferencepattern produced by a portion of said set of all modulated object beamsand of said set of all modulated reference beams pairwise, all suchpairs being mutually incoherent with respect to one another; (f) meansfor directing said portion of said set of modulated object beams and ofsaid set of modulated reference beams onto said holographic medium andfor interfering said portion of said set of modulated object beams andof said set of modulated reference beams, pairwise, inside saidholographic medium; and (g) means for blocking said set of object beamssuch that at least a portion of said set of modulated reference beamsreconstruct a set of stored holographic interference patterns as a setof output beams.
 20. The apparatus of claim 19 wherein said array ofcoherent light sources comprises a two-dimensional array of saidsources.
 21. The apparatus of claim 19 wherein said array of coherentlight sources comprises an array of semiconductor laser diodes, eachlaser itself coherent, and each laser operating incoherently withrespect to the other lasers.
 22. The apparatus of claim 19 wherein eachsaid set of multiplexed object beams and each said set of multiplexedreference beams is independently multiplexed in at least one of angle,space, and wavelength.
 23. The apparatus of claim 22 in which eachobject beam of a pair is at a separate, first given angle, and itsassociated mutually coherent reference beam is at a separate, secondgiven angle.
 24. The apparatus of claim 23 wherein said set of outputbeams is angularly multiplexed and detected in such a manner as toproduce an incoherent summation on a pixel-by-pixel basis of the set ofreconstructed images formed from said set of output beams.
 25. Theapparatus of claim 19 wherein each object beam is spatially modulated sothat all object beams are identically modulated and each reference beamis independently modulated.
 26. The apparatus of claim 19 wherein eachobject beam is spatially modulated so that all object beams areidentically modulated and each reference beam is spatially modulated sothat all reference beams are identically modulated.
 27. The apparatus ofclaim 19 wherein each object beam is independently modulated and eachreference beam is spatially modulated so that all reference beams areidentically modulated.
 28. The apparatus of claim 19 wherein each objectbeam is independently modulated and each reference beam is independentlymodulated.
 29. The apparatus of claim 19 wherein at least one of saidmeans for modulating said object beam and said means for modulating saidreference beam comprises a spatial light modulator.
 30. The apparatus ofclaim 29 wherein said spatial light modulator comprises an array ofintegrated optical detectors, optical modulators, and electronics, saiddetectors capable for detecting at least one control beam incidentthereon to generate a detected signal, said electronics capable ofprocessing said detected signal and controlling the amount of modulationof said modulators, and said modulators capable of modulating one ofsaid sets of beams.
 31. The apparatus of claim 19 further includingmeans for selecting at least a portion of said set of modulated objectbeams and of said set of modulated reference beams, said portion of saidsets selected prior to forming said interference pattern.
 32. Theapparatus of claim 31 wherein said selecting means is provided byindependent control of said coherent sources of said array.
 33. Theapparatus of claim 19 wherein said holographic medium comprises aphotorefractive material capable of real-time recording andreconstruction of holographic images.
 34. The apparatus of claim 19further including means for directing said set of output beams so thatsaid reconstructions of said stored holographic interference patternsare incoherently superimposed in space.
 35. Apparatus for providingmultiplexed volume holographic recording and readout comprising:(a)means for providing an array of coherent light sources that are mutuallyincoherent, said array of coherent light sources comprising an array ofsemiconductor laser diodes, each laser itself coherent, and each laserincoherent with respect to the other lasers; (b) means for forming anobject beam and a reference beam from each coherent light source,thereby forming a set of angularly multiplexed object beams and aseparate set of angularly multiplexed reference beams; (c) means forspatially modulating each object beam so that all object beams areidentically modulated, said means comprising a first spatial lightmodulator; (d) means for independently modulating each reference beam,said means comprising a second spatial light modulator; (e) aholographic medium capable of simultaneously recording therein aholographic interference pattern produced by a portion of said set ofall modulated object beams and of said set of all modulated referencebeams pairwise, each object beam of a pair at a separate, first givenangle, and its associated mutually coherent reference beam at aseparate, second given angle, all such pairs being mutually incoherentwith respect to one another; (f) means for directing said portion ofsaid set of modulated object beams and of said set of modulatedreference beams onto said holographic medium and for interfering saidportion of said set of modulated object beams and of said set ofmodulated reference beams, pairwise, inside said holographic medium; and(g) means for blocking said set of object beams such that at least aportion of said set of modulated reference beams reconstruct a set ofstored holographic interference patterns as a set of output beams. 36.The apparatus of claim 35 wherein said holographic medium comprises aphotorefractive material capable of real-time recording andreconstruction of holographic images.
 37. The apparatus of claim 35wherein transmittance of the modulator of each pixel of said spatiallight modulator is encoded onto a set of angularly multiplexed objectbeams.
 38. The apparatus of claim 35 further including means forselecting at least a portion of said set of modulated object beams andof said set of modulated reference beams, said portions of said setsselected prior to forming said interference pattern.
 39. The apparatusof claim 35 further including means for directing said set of outputbeams so that said reconstructions of said stored holographicinterference patterns are incoherently superimposed in space. 40.Apparatus for a neural network comprising:(a) means for providing anarray of coherent light sources that are mutually incoherent; (b) meansfor simultaneously forming an object beam and a reference beam from eachcoherent light source, thereby forming a set of object beams that aremultiplexed in at least one of angle and space and a separate set ofreference beams that are multiplexed in at least one of angle and space;(c) means for modulating each object beam; (d) means for modulating eachreference beam, with the proviso that at least one of said sets of beamsis spatially and identically modulated; (e) a holographic medium capableof simultaneously recording therein a holographic interference patternproduced by at least a portion of said set of all modulated object beamsand of said set of all modulated reference beams pairwise, all suchpairs being mutually incoherent with respect to one another; and (f)means for directing said portion of said set of modulated object beamsand of said set of modulated reference beams onto said holographicmedium and for interfering said portion of said set of modulated objectbeams and of said set of modulated reference beams, pairwise, insidesaid holographic medium.
 41. The apparatus of claim 40 further includingmeans for blocking said set of object beams such that said set ofreference beams reconstructs a stored holographic interference patternas a set of output beams, which are detected in such a manner as toproduce an incoherent summation on a pixel-by-pixel basis of the set ofreconstructed images formed from said set of output beams.
 42. Theapparatus of claim 40 further including means for modifying at least aportion of said set of object beams in response to at least one of atleast a portion of said reconstructed images and a set ofexternally-supplied signals.
 43. The apparatus of claim 40 wherein saidarray of coherent light sources comprises a two-dimensional array ofsaid sources.
 44. The apparatus of claim 40 wherein said array ofcoherent light sources comprises an array of semiconductor laser diodes,each laser itself coherent, and each laser incoherent with respect tothe other lasers.
 45. The apparatus of claim 40 wherein each object beamis spatially modulated so that all object beams are identicallymodulated and each reference beam is independently modulated.
 46. Theapparatus of claim 40 wherein each object beam is spatially modulated sothat all object beams are identically modulated and each reference beamis spatially modulated so that all reference beams are identicallymodulated.
 47. The apparatus of claim 40 wherein each object beam isindependently modulated and each reference beam is spatially modulatedso that all reference beams are identically modulated.
 48. The apparatusof claim 40 wherein at least one of said means for modulating saidobject beam and said means for modulating said reference beam comprisesa spatial light modulator.
 49. The apparatus of claim 48 wherein saidspatial light modulator comprises an array of optical detectors, opticalmodulators, and electronics, said detectors capable for detecting atleast one control beam incident thereon to generate a detected signal,said electronics capable of processing said detected signal andcontrolling the amount of modulation of said modulators, and saidmodulators capable of modulating one of said sets of beams.
 50. Theapparatus of claim 40 further including means for selecting at least aportion of said set of modulated object beams and of said set ofmodulated reference beams, said portion of said sets selected prior toforming said interference pattern.
 51. The apparatus of claim 50 whereinsaid selecting means is provided by independent control of said coherentsources of said array.
 52. The apparatus of claim 40 wherein saidholographic medium comprises a photorefractive material capable ofreal-time recording and reconstruction of holographic images.
 53. Theapparatus of claim 40 wherein interconnection weights stored in saidholographic medium are updated according to the equation

    Δw.sub.ij =αx.sub.j δ.sub.i -βw.sub.ij,

where Δw_(ij) is the weight update given by w_(ij) (k+1)-w_(ij) (k),x_(j) is the input to the interconnection layer, δ_(i) is the trainingterm, and α, which is greater than zero, and β, which is non-negative,are constants.
 54. The apparatus of claim 40 wherein interconnectionweights stored in said holographic medium are updated according to theequation

    Δw.sub.ij ≈αsgn(x.sub.j δ.sub.i)(|x.sub.j δ.sub.i |).sup.1/2,

where Δw_(ij) is the weight update given by w_(ij) (k+1)-w_(ij) (k),x_(j) is the input to the interconnection layer, δ_(i) is the trainingterm, and sgn(u)=1 if u>0, 0 if u=0, and -1 if u<0.
 55. The apparatus ofclaim 40 wherein each object beam is independently modulated and eachreference beam is independently modulated.
 56. The apparatus of claim 40further including means for modifying at least a portion of said set ofreference beams in response to at least one of at least a portion ofsaid reconstruction pattern and a set of externally-applied signals. 57.The apparatus of claim 40 further including means for splitting at leasta portion of said set of modulated reference beams into a set ofsubstantially identical modulated reference beams and a set of secondarybeams, said secondary beams being directed onto a secondary hologram.58. The apparatus of claim 57 further including means for modifying atleast a portion of said set of reference beams in response to at least aportion of a set of beams emanating from said secondary hologram inresponse to said set of secondary beams.
 59. The apparatus of claim 58in which said secondary hologram is dynamically modifiable as a functionof its input beams and externally-applied signals.
 60. The apparatus ofclaim 40 further including means for blocking said set of referencebeams.
 61. The apparatus of claim 40 wherein said set of modulatedobject beams gives rise to a set of output error beams, emanating fromthe holographic medium, and including means for modifying at least aportion of said set of object beams in response to said set of outputerror beams.
 62. The apparatus of claim 40 wherein said set of modulatedobject beams gives rise to a set of output error beams, emanating fromthe holographic medium, and including means for modifying at least aportion of the set of object beams of an additional apparatus of claim40.
 63. The apparatus of claim 40 wherein each object beam of a pair isat a separate, first given angle, and its associated mutually coherentreference beam is at a separate, second given angle.
 64. Apparatus fordigital computing and telecommunication interconnection, switching, androuting comprising:(a) means for providing an array of coherent lightsources that are mutually incoherent; (b) means for simultaneouslyforcing an object beam and a reference beam from each coherent lightsource, thereby forming a set of multiplexed object beams and a separateset of multiplexed reference beams; (c) means for modulating each objectbeam; (d) means for modulating each reference beam; (e) a holographicmedium capable of simultaneously recording therein a holographicinterference pattern produced by at least a portion of said set of allmodulated multiplexed object beams and of said set of all modulatedreference beams pairwise, all such pairs being mutually incoherent withrespect to one another; (f) means for directing at least a portion ofsaid set of modulated object beams and of said set of modulatedreference beams onto said holographic medium and for interfering saidportion of said set of modulated object beams and of said set ofmodulated reference beams, pairwise, inside said holographic medium; (g)means for providing an array of optical data inputs and for providing anarray of optical data output receivers; (h) means for directing theinput light from said array of optical inputs to said holographic mediumsuch that said input light Bragg matches to corresponding saidholographic interference patterns, producing a set of output beams; and(i) means for directing said set of output beams to said optical dataoutput receivers.
 65. The apparatus of claim 64 wherein at least aportion of said array of light sources have slightly differentwavelengths.
 66. The apparatus of claim 65 wherein said array of opticaldata inputs and said array of optical data output receivers eachcomprise a one-dimensional array of wavelength division multiplexedoptical input/output lines.
 67. The apparatus of claim 66 wherein saidsource array comprises a two-dimensional array of coherent sources, withslightly different wavelengths in one dimension and mutually incoherentin the orthogonal dimension.
 68. The apparatus of claim 65 wherein saidarray of optical data inputs and said array of optical data outputreceivers each comprise a two-dimensional array of wavelength divisionmultiplexed optical input/output lines.
 69. The apparatus of claim 68wherein said source array comprises a two-dimensional array of sources,such that a set of individually coherent beams, multiplexed inwavelength, is transmitted by each pixel of said array of sources. 70.The apparatus of claim 64 wherein each said set of multiplexed objectbeams and each said set of multiplexed reference beams is independentlymultiplexed in at least one of angle, space, and wavelength.
 71. Theapparatus of claim 70 wherein each object beam of a pair is at aseparate, first given angle, and its associated mutually coherentreference beam is at a separate, second given angle.
 72. The apparatusof claim 64 wherein each object beam is spatially modulated so that allobject beams ar identically modulated and each reference beam isindependently modulated.
 73. The apparatus of claim 64 wherein eachobject beam is spatially modulated so that all object beams areidentically modulated and each reference beam is spatially modulated sothat all reference beams are identically modulated.
 74. The apparatus ofclaim 64 wherein each object beam is independently modulated and eachreference beam is spatially modulated so that all reference beams areidentically modulated.
 75. The apparatus of claim 64 wherein each objectbeam is independently modulated and each reference beam is independentlymodulated.
 76. The apparatus of claim 64 wherein at least one of saidmeans for modulating said object beam and said means for modulating saidreference beam comprises a spatial light modulator.
 77. The apparatus ofclaim 76 wherein said spatial light modulator comprise an array ofintegrated optical detectors, optical modulators, and electronics, saiddetectors capable of detecting at least one control beam incidentthereon to generate a detected signal, said electronics capable ofprocessing said detected signal and controlling the amount of modulationof said modulators, and said modulators capable of modulating one ofsaid sets of beams.
 78. The apparatus of claim 64 further includingmeans for selecting at least a portion of said set of modulated objectbeams and of said set of modulated reference beams, said portions ofsaid sets selected prior to forming said interference pattern.
 79. Theapparatus of claim 78 wherein said selecting means is provided byindependent control of said coherent sources of said array.
 80. Theapparatus of claim 64 wherein said holographic medium comprises aphotorefractive material capable of real-time recording andreconstruction of holographic images.
 81. The apparatus of claim 64wherein transmittance of the modulator of each pixel of at least onespatial light modulator is encoded onto a set of angularly multiplexedobject beams.
 82. The apparatus of claim 64 further including means forblocking said set of object beams.
 83. The apparatus of claim 64 furtherincluding means for blocking said set of reference beams.
 84. Apparatusfor providing multiplexed volume holographic recording of multiplexedvolume holographic optical elements comprising:(a) means for providingan array of coherent light sources that are mutually incoherent; (b)means for simultaneously forming an object beam and a reference beamfrom each coherent light source, thereby forming a set of multiplexedobject beams and a separate set of multiplexed reference beams; (c)means for modulating at least one of said set of object beams and saidset of reference beams; (d) a holographic medium capable ofsimultaneously recording therein a holographic interference patternproduced by at least a portion of said set of all multiplexed objectbeams and of said set of all multiplexed reference beams pairwise, allsuch pairs being mutually incoherent with respect to one another; (e)means for directing at least a portion of said set of reference beamsonto said holographic medium in such a way as to approximate thereference beam phase fronts that are to be incident during readout; and(f) means for directing at least a portion of said set of object beamsonto said holographic medium and for interfering said portion of saidset of object beams and of said set of reference beams, pairwise, insidesaid holographic medium.
 85. The apparatus of claim 84 wherein each saidset of multiplexed object beams and each said set of multiplexedreference beams is independently multiplexed in at least one of angle,space, and wavelength.
 86. The apparatus of claim 85 wherein each objectbeam of a pair is at a separate, first given angle, and its associatedmutually coherent reference beam is at a separate, second given angle.87. The apparatus of claim 84 wherein each object beam is spatiallymodulated so that all object beams are identically modulated and eachreference beam is independently modulated.
 88. The apparatus of claim 84further comprising means for blocking said set of object beams such thatat least a portion of said set of reference beams reconstructs a set ofstored holographic interference patterns as a set of output beams. 89.The apparatus of claim 84 wherein each object beam is spatiallymodulated so that all object beams are identically modulated and eachreference beam is spatially modulated so that all reference beams areidentically modulated.
 90. The apparatus of claim 84 wherein each objectbeam is independently modulated and each reference beam is spatiallymodulated so that all reference beams are identically modulated.
 91. Theapparatus of claim 84 wherein each object beam is independentlymodulated and each reference beam is independently modulated.
 92. Theapparatus of claim 84 wherein at least one of said means for modulatingsaid object beam and said means for modulating said reference beamcomprises a spatial light modulator.
 93. The apparatus of claim 84wherein said means for modulating incorporates the spatial modulation ofat least one of amplitude and phase.
 94. The apparatus of claim 84wherein said means for modulating comprises at least one of a staticmicrolens array and a dynamic microlens array.
 95. The apparatus ofclaim 84 further including means for selecting at least a portion ofsaid set of object beams and of said set of reference beams, saidportions of said sets selected prior to forming said interferencepattern.
 96. The apparatus of claim 95 wherein said selecting means isprovided by independent control of said coherent sources of said array.97. Apparatus for copying an original multiplexed volume hologram toform a substantially identical multiplexed volume hologramcomprising:(a) means for providing an array of coherent light sourcesthat are mutually incoherent; (b) means for forming two reference beamsfrom each coherent light source, thereby forming two sets of multiplexedreference beams, each set at a different location; (c) means fordirecting said first set of reference beams onto said originalmultiplexed volume hologram to thereby form a set of output beams; (d)means for directing said second set of reference beams onto a secondaryholographic recording medium; (e) means for directing said set of outputbeams from said original multiplexed volume hologram onto said secondaryholographic recording medium, with path lengths sufficiently identicalto the reference beam path lengths to permit coherent interference,pairwise, between said output beams and said second set of referencebeams, inside said secondary holographic recording medium; and (f) meansfor simultaneously recording in said secondary holographic medium aholographic interference pattern produced by said set of output beamsand said second set of reference beams, thereby forming saidsubstantially identical multiplexed volume hologram.
 98. The apparatusof claim 97 wherein said second set of reference beams is incident onsaid secondary holographic recording medium with substantially identicalamplitude and phase as said first set of reference beams is incident onsaid original multiplexed volume hologram.
 99. The apparatus of claim 97wherein said set of output beams is incident on said secondaryholographic recording medium with substantially identical amplitude andphase as original set of object beams was incident on said originalmultiplexed volume hologram during its recording.
 100. The apparatus ofclaim 80 further including means for independent modulation of saidsources in said source array.
 101. The apparatus of claim 97 whereinsaid sets of reference beams are multiplexed in at least one of angle,space, and wavelength.
 102. The apparatus of claim 97 wherein said setof output beams is incident on said secondary holographic recordingmedium with substantially identical amplitude and phase as original setof object beams was incident on said original multiplexed volumehologram during its recording except for a magnification ordemagnification of said amplitude or incident beam angle.
 103. Theapparatus of claim 97 wherein said second set of reference beams isincident on said secondary holographic recording medium withsubstantially identical amplitude and phase as said first set ofreference beams was incident on said original multiplexed volumehologram during its recording, except for a magnification ordemagnification of said amplitude or incident beam angle.